Trigonometry prove questions class 10

Trigonometric identities are equalities involving trigonometric functions. An example of a trigonometric identity is \[\sin^2 \theta + \cos^2 \theta = 1.\] In order to prove trigonometric identities, we generally use other known identities such as Prove that \((1 - \sin x) (1 +\csc x) =\cos x \cot x.\) We have \[(1 - \sin x) (1 +\csc x)=(1 - \sin x)\left(1 + \frac\] Proving a trigonometric identity refers to showing that the identity is always true, no matter what value of \( x \) or \( \theta \) is used. Because it has to hold true for all values of \(x\), we cannot simply substitute in a few values of \(x\) to "show" that they are equal. It is possible that both sides are equal at several values (namely when we solve the equation), and we might falsely think that we have a true identity. Instead, we have to use logical steps to show that one side of the equation can be transformed to the other side of the equation. Sometimes, we will work separately on each side, till they meet in the middle. You should be familiar with the various trigonometric identities, like the There are many different ways to prove an identity. Here are some guidelines in case you get stuck: 1) Work on the side that is more complicated. Try and simplify it. 2) Replace all trigonometric functions with just \( \sin \theta \) and \( \cos \theta \) where possible. 3) Identify algebraic operations like factoring, expanding, distributive property, adding and multiplying fractions. This allows us to simpl...

Trigonometry Questions Trigonometry questions given here involve finding the missing sides of a triangle with the help of trigonometric ratios and proving trigonometry identities. We know that trigonometry is one of the most important chapters of Class 10 Maths. Hence, solving these questions will help you to improve your problem-solving skills. What is Trigonometry? The word ‘trigonometry’ is derived from the Greek words ‘tri’ (meaning three), ‘gon’ (meaning sides) and ‘metron’ (meaning measure). Trigonometry is the study of relationships between the sides and angles of a triangle. The basic sine of ∠A = sin A = Side opposite to ∠A/ Hypotenuse cosine of ∠A = cos A = Side adjacent to ∠A/ Hypotenuse tangent of ∠A = tan A = (Side opposite to ∠A)/ (Side adjacent to ∠A) cosecant of ∠A = cosec A = 1/sin A = Hypotenuse/ Side opposite to ∠A secant of ∠A = sec A = 1/cos A = Hypotenuse/ Side adjacent to ∠A cotangent of ∠A = cot A = 1/tan A = (Side adjacent to ∠A)/ (Side opposite to ∠A) Also, tan A = sin A/cos A cot A = cos A/sin A Also, read: Trigonometry Questions and Answers 1. From the given figure, find tan P – cot R. Solution: From the given, PQ = 12 cm PR = 13 cm In the right triangle PQR, Q is right angle. By Pythagoras theorem, PR 2 = PQ 2 + QR 2 QR 2 = (13) 2– (12) 2 = 169 – 144 = 25 QR = 5 cm tan P = QR/PQ = 5/12 cot R = QR/PQ = 5/12 So, tan P – cot R = (5/12) – (5/12) = 0 Trigonometric ratios of complementary angles: sin (90° ...

RD Sharma Solutions Class 10 Maths Chapter 6 – Free PDF Download RD Sharma Solutions for Class 10 Maths Chapter 6 – Trigonometric Identities are provided here. The branch of Mathematics which deals with the measurement of the sides and the angles of a triangle is known as trigonometry . Students who find it difficult to understand the concepts covered in this chapter can make their learning process smooth and easy using RD Sharma Solutions . These solutions are well structured by our subject expert team at BYJU’S to help students grasp the in-depth knowledge of concepts which are vital for examinations. Trigonometric Identities is the 6th Chapter of RD Sharma Solutions Class 10 . This chapter consists of two exercises. Students can find the precise answers for these exercises in RD Sharma Solutions for Class 10 . The previous chapter was about trigonometric ratios and the relations between them. But this chapter explains the trigonometric identities in a comprehensive manner in accordance with the student’s intelligence quotient. Previous Next Access the RD Sharma Solutions for Class 10 Maths Chapter 6 – Trigonometric Identities RD Sharma Solutions for Class 10 Maths Chapter 6 Exercise 6.1 Page No: 6.43 Prove the following trigonometric identities: 1. (1 – cos 2 A) cosec 2 A = 1 Solution: Taking the L.H.S., (1 – cos 2 A) cosec 2 A = (sin 2 A) cosec 2 A [∵ sin 2 A + cos 2 A = 1 ⇒1 – sin 2 A = cos 2 A] = 1 2 = 1 = R.H.S. – Hence, proved. 2. (1 + cot 2A) sin 2A = 1 Solution: ...

CBSE Study Material • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry NCERT Solutions For Class 10 Maths Chapter 8 – Download Free PDF NCERT Solutions for Class 10 Maths Chapter 8 Introduction to Trigonometry is helpful for the students as it aids in understanding the concepts as well as in scoring well in CBSE Class 10 board examination. The NCERT Solutions are designed and reviewed by subject experts and cover all the questions from the textbook. These The NCERT Solutions for Class 10 Maths provide a strong foundation for every concept across all chapters. Students can clarify their doubts and understand the fundamentals of this chapter. Also, students can solve the difficult problems in each exercise with the help of these

According to J.F. Herbart “There is perhaps nothing which occupies the middle position of mathematics as trigonometry". From the statement itself we can guess that what a great or important role trigonometry plays in Mathematics. Let’s start from the beginning and learn how interesting it is. Trigonometry is basically the measuring of sides, angles and other things involved in a triangle and here we will deal with right angle triangle, the angles involved and many other things. Trigonometry is derived from Greek words “tri" means three “gon" means sides and “metron" means measurements. Here we will study the different Trigonometric Ratios different terms identities related to Trigonometry. Trigonometric Ratios Here in any right angle triangle we define 6 trigonometric ratios which are Sine, Cosine, Tangent, Secant, Cosecant, and Cotangent. So, the trigonometric ratios of an acute angle in a right triangle express the relationship between the angle and the length of its sides. For any Triangle ABC we define the trignometric ratios as: Example 1 : Find the value of all trigonometric ratios at angle A, if in any triangle ABC right angled at B AB=24, BC=7. Solution : For any right angled triangle using Pythagoras theorem we get AB 2+BC 2=AC 2 24 2+7 2= AC 2 and hence AC =25. Therefore from the figure Sin A = 7/25 Cosec A = 25/7 Cos A = 24/25 Sec A = 25/24 Tan A = 7/24 Cot A = 24/7 Trigonometric Ratios for some specific Angles If we take a triangle ABC and then if we assign the...

Trigonometry Problems and Questions with Solutions - Grade 10 Trigonometry Problems and Questions with Solutions - Grade 10 Grade 10 Problems • Find x and H in the right triangle below. • Find the lengths of all sides of the right triangle below if its area is 400. • BH is perpendicular to AC. Find x the length of BC. • ABC is a right triangle with a right angle at A. Find x the length of DC. • In the figure below AB and CD are perpendicular to BC and the size of angle ACB is 31°. Find the length of segment BD. • The area of a right triangle is 50. One of its angles is 45°. Find the lengths of the sides and hypotenuse of the triangle. • In a right triangle ABC, tan(A) = 3/4. Find sin(A) and cos(A). • In a right triangle ABC with angle A equal to 90°, find angle B and C so that sin(B) = cos(B). • A rectangle has dimensions 10 cm by 5 cm. Determine the measures of the angles at the point where the diagonals intersect. • The lengths of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The size of angle C is 59°. Find the length of side AC. • From the top of a 200 meters high building, the angle of depression to the bottom of a second building is 20 degrees. From the same point, the angle of elevation to the top of the second building is 10 degrees. Calculate the height of the second building. • Karla is riding vertically in a hot air balloon, directly over a point P on the ground. Karla spots a parked car on the ground at an angle of depression of...

Search for: • MCQ Questions Expand / Collapse • MCQ Questions for Class 12 • MCQ Questions for Class 11 • MCQ Questions for Class 10 • MCQ Questions for Class 9 • MCQ Questions for Class 8 • MCQ Questions for Class 7 • MCQ Questions for Class 6 • Extra Questions • CBSE Notes • NCERT Solutions Expand / Collapse • RS Aggarwal Solutions • RD Sharma Solutions • ML Aggarwal Solutions • CBSE MCQ • CBSE Sample Papers Expand / Collapse • English Grammar • English Summaries • Unseen Passages • MCQ Questions • MCQ Questions for Class 12 • MCQ Questions for Class 11 • MCQ Questions for Class 10 • MCQ Questions for Class 9 • MCQ Questions for Class 8 • MCQ Questions for Class 7 • MCQ Questions for Class 6 • Extra Questions • CBSE Notes • NCERT Solutions • RS Aggarwal Solutions • RD Sharma Solutions • ML Aggarwal Solutions • CBSE MCQ • CBSE Sample Papers • English Grammar • English Summaries • Unseen Passages Here we are providing Introduction to Trigonometry Class 10 Extra Questions Maths Chapter 8 with Answers Solutions, Extra Questions for Class 10 Maths Introduction to Trigonometry with Answers Solutions Extra Questions for Class 10 Maths Chapter 8 Introduction to Trigonometry with Solutions Answers Introduction to Trigonometry Class 10 Extra Questions Short Answer Type 1 Trigonometry Class 10 Extra Questions Question 1. Find maximum value of \(\frac

RD Sharma Solutions Class 10 Maths Chapter 6 – Free PDF Download RD Sharma Solutions for Class 10 Maths Chapter 6 – Trigonometric Identities are provided here. The branch of Mathematics which deals with the measurement of the sides and the angles of a triangle is known as trigonometry . Students who find it difficult to understand the concepts covered in this chapter can make their learning process smooth and easy using RD Sharma Solutions . These solutions are well structured by our subject expert team at BYJU’S to help students grasp the in-depth knowledge of concepts which are vital for examinations. Trigonometric Identities is the 6th Chapter of RD Sharma Solutions Class 10 . This chapter consists of two exercises. Students can find the precise answers for these exercises in RD Sharma Solutions for Class 10 . The previous chapter was about trigonometric ratios and the relations between them. But this chapter explains the trigonometric identities in a comprehensive manner in accordance with the student’s intelligence quotient. Previous Next Access the RD Sharma Solutions for Class 10 Maths Chapter 6 – Trigonometric Identities RD Sharma Solutions for Class 10 Maths Chapter 6 Exercise 6.1 Page No: 6.43 Prove the following trigonometric identities: 1. (1 – cos 2 A) cosec 2 A = 1 Solution: Taking the L.H.S., (1 – cos 2 A) cosec 2 A = (sin 2 A) cosec 2 A [∵ sin 2 A + cos 2 A = 1 ⇒1 – sin 2 A = cos 2 A] = 1 2 = 1 = R.H.S. – Hence, proved. 2. (1 + cot 2A) sin 2A = 1 Solution: ...

Trigonometry Questions Trigonometry questions given here involve finding the missing sides of a triangle with the help of trigonometric ratios and proving trigonometry identities. We know that trigonometry is one of the most important chapters of Class 10 Maths. Hence, solving these questions will help you to improve your problem-solving skills. What is Trigonometry? The word ‘trigonometry’ is derived from the Greek words ‘tri’ (meaning three), ‘gon’ (meaning sides) and ‘metron’ (meaning measure). Trigonometry is the study of relationships between the sides and angles of a triangle. The basic sine of ∠A = sin A = Side opposite to ∠A/ Hypotenuse cosine of ∠A = cos A = Side adjacent to ∠A/ Hypotenuse tangent of ∠A = tan A = (Side opposite to ∠A)/ (Side adjacent to ∠A) cosecant of ∠A = cosec A = 1/sin A = Hypotenuse/ Side opposite to ∠A secant of ∠A = sec A = 1/cos A = Hypotenuse/ Side adjacent to ∠A cotangent of ∠A = cot A = 1/tan A = (Side adjacent to ∠A)/ (Side opposite to ∠A) Also, tan A = sin A/cos A cot A = cos A/sin A Also, read: Trigonometry Questions and Answers 1. From the given figure, find tan P – cot R. Solution: From the given, PQ = 12 cm PR = 13 cm In the right triangle PQR, Q is right angle. By Pythagoras theorem, PR 2 = PQ 2 + QR 2 QR 2 = (13) 2– (12) 2 = 169 – 144 = 25 QR = 5 cm tan P = QR/PQ = 5/12 cot R = QR/PQ = 5/12 So, tan P – cot R = (5/12) – (5/12) = 0 Trigonometric ratios of complementary angles: sin (90° ...

Trigonometric identities are equalities involving trigonometric functions. An example of a trigonometric identity is \[\sin^2 \theta + \cos^2 \theta = 1.\] In order to prove trigonometric identities, we generally use other known identities such as Prove that \((1 - \sin x) (1 +\csc x) =\cos x \cot x.\) We have \[(1 - \sin x) (1 +\csc x)=(1 - \sin x)\left(1 + \frac\] Proving a trigonometric identity refers to showing that the identity is always true, no matter what value of \( x \) or \( \theta \) is used. Because it has to hold true for all values of \(x\), we cannot simply substitute in a few values of \(x\) to "show" that they are equal. It is possible that both sides are equal at several values (namely when we solve the equation), and we might falsely think that we have a true identity. Instead, we have to use logical steps to show that one side of the equation can be transformed to the other side of the equation. Sometimes, we will work separately on each side, till they meet in the middle. You should be familiar with the various trigonometric identities, like the There are many different ways to prove an identity. Here are some guidelines in case you get stuck: 1) Work on the side that is more complicated. Try and simplify it. 2) Replace all trigonometric functions with just \( \sin \theta \) and \( \cos \theta \) where possible. 3) Identify algebraic operations like factoring, expanding, distributive property, adding and multiplying fractions. This allows us to simpl...