Trigonometry hardest questions class 10

Solution : L.H.S : = (tan 2 θ - 1)/(tan 2 θ + 1) = [(sin 2 θ/cos 2 θ) - 1] / [(sin 2 θ/cos 2 θ) + 1] = [(sin 2θ - cos 2 θ) /cos 2 θ] / [(sin 2 θ + cos 2 θ) /cos 2 θ] = [(sin 2θ -cos 2θ)/cos 2θ] ⋅ [ cos 2 θ/1] = sin 2θ -cos 2θ = 1 - cos 2θ -cos 2θ = 1 - 2 cos 2 θ R.H.S Hence proved. Question 2 : Prove that Solution : [(1 + sin θ - cos θ)/(1 + sin θ + cos θ)] 2 =[(1 + sin θ) - cos θ] 2/[(1 + sin θ) + cos θ] 2 Expanding the numerator and denominator using the formula (a - b) 2 and (a + b) 2 =[(1+sinθ) 2+cos 2θ - 2(1+sin θ)cos θ] / [(1+sinθ) 2+cos 2θ + 2(1+sin θ)cos θ] Numerator : (1 + sinθ) 2+ cos 2θ - 2(1 + sin θ)cos θ = 1 + sin 2θ + 2sinθ + cos 2θ - 2cos θ - 2cos θ sin θ = 1 + (sin 2θ + cos 2θ) + 2sinθ - 2cos θ - 2cos θ sin θ = 2 + 2sinθ - 2cos θ - 2cos θ sin θ = 2(1 + sinθ - cos θ - cos θ sin θ) = 2 [(1 + sinθ) - cos θ(1 + sinθ)] = 2 [(1 + sinθ) (1 - cos θ)] -----(1) Denominator : [(1+sinθ) 2+cos 2θ + 2(1+sin θ)cos θ] = 1 + sin 2θ + 2sinθ + cos 2θ + 2cos θ + 2cos θ sin θ = 1 + (sin 2θ + cos 2θ) + 2sinθ + 2cos θ + 2cos θ sin θ = 2 + 2sinθ + 2cos θ + 2cos θ sin θ = 2(1 + sinθ + cos θ + cos θ sin θ) = 2 [(1 + sinθ) + cos θ(1 + sinθ)] = 2 [(1 + sinθ) (1 + cos θ)] -----(2) (1)/(2) = = (1 - cos θ)/ (1 + cos θ) Hence proved. Question 3 : If x sin 3 θ+ y cos 3 θ = sin θcos θand x sin θ= y cos θ, then prove that x 2 +y 2 = 1 . Solution : x sinθ (sin 2 θ) + (y cosθ)cos 2 θ = sinθcosθ x sinθ (sin 2 θ) + (x sinθ) cos 2 θ = sinθcosθ Since x sinθ = y cosθ x sinθ (sin 2 θ + cos 2 θ) = s...

This class 10 Maths extra practice question is from chapter 8 - Introduction to Trigonometry. Concept Covered: Computing the value of angle by solving a trigonometric expression using Componendo Dividendo Rule. Level of difficulty: Hard Question 14: If θ is an acute angle and \\frac), find θ Explanatory Answer | Trigonometry Important Question 14 What is Componendo Dividendo Rule? If \\frac) ∴ sin θ = sin 60° θ = 60°

Please refer to the MCQ Questions for Class 10 Maths Trigonometry with Answers. The following Trigonometry Class 10 Maths MCQ Questions have been designed based on the current academic year syllabus and examination guidelines for Class 10. Our faculty has designed Trigonometry Class 10 MCQ Questions with Answers Please see below Trigonometry Class 10 Mathematics Question.If tan A= 3/4, then the value of sec A is 1v (a) 5/3 (b) 5/4 (c) 4/3 (d) 4/5 B Question. In the following questions, a statement of assertion (A) is followed by a statement reason (R). Choose the correct choice as: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true. 1. Assertion (A): sin 267° + cos 267° = 1. Reason (R): For any value of q, sin 2θ + cos 2θ = 1. 2. Assertion (A): The value of sec 210° – cot 280° is 1. Reason (R): The value of sin 30° = 1/ 2 Related Posts: • Notes And Questions For NCERT Class 10 Mathematics… • MCQs for NCERT Class 10 Science Chapter 6 Life Processes • NCERT Solutions For Class 3 to 12 • MCQs For NCERT Class 11 Maths Trigonometric Functions With… • NCERT Books Download PDF Class 1 to 12 • Inverse Trigonometric Functions Class 12 Mathematics Exam…

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...

Solution : L.H.S : = (tan 2 θ - 1)/(tan 2 θ + 1) = [(sin 2 θ/cos 2 θ) - 1] / [(sin 2 θ/cos 2 θ) + 1] = [(sin 2θ - cos 2 θ) /cos 2 θ] / [(sin 2 θ + cos 2 θ) /cos 2 θ] = [(sin 2θ -cos 2θ)/cos 2θ] ⋅ [ cos 2 θ/1] = sin 2θ -cos 2θ = 1 - cos 2θ -cos 2θ = 1 - 2 cos 2 θ R.H.S Hence proved. Question 2 : Prove that Solution : [(1 + sin θ - cos θ)/(1 + sin θ + cos θ)] 2 =[(1 + sin θ) - cos θ] 2/[(1 + sin θ) + cos θ] 2 Expanding the numerator and denominator using the formula (a - b) 2 and (a + b) 2 =[(1+sinθ) 2+cos 2θ - 2(1+sin θ)cos θ] / [(1+sinθ) 2+cos 2θ + 2(1+sin θ)cos θ] Numerator : (1 + sinθ) 2+ cos 2θ - 2(1 + sin θ)cos θ = 1 + sin 2θ + 2sinθ + cos 2θ - 2cos θ - 2cos θ sin θ = 1 + (sin 2θ + cos 2θ) + 2sinθ - 2cos θ - 2cos θ sin θ = 2 + 2sinθ - 2cos θ - 2cos θ sin θ = 2(1 + sinθ - cos θ - cos θ sin θ) = 2 [(1 + sinθ) - cos θ(1 + sinθ)] = 2 [(1 + sinθ) (1 - cos θ)] -----(1) Denominator : [(1+sinθ) 2+cos 2θ + 2(1+sin θ)cos θ] = 1 + sin 2θ + 2sinθ + cos 2θ + 2cos θ + 2cos θ sin θ = 1 + (sin 2θ + cos 2θ) + 2sinθ + 2cos θ + 2cos θ sin θ = 2 + 2sinθ + 2cos θ + 2cos θ sin θ = 2(1 + sinθ + cos θ + cos θ sin θ) = 2 [(1 + sinθ) + cos θ(1 + sinθ)] = 2 [(1 + sinθ) (1 + cos θ)] -----(2) (1)/(2) = = (1 - cos θ)/ (1 + cos θ) Hence proved. Question 3 : If x sin 3 θ+ y cos 3 θ = sin θcos θand x sin θ= y cos θ, then prove that x 2 +y 2 = 1 . Solution : x sinθ (sin 2 θ) + (y cosθ)cos 2 θ = sinθcosθ x sinθ (sin 2 θ) + (x sinθ) cos 2 θ = sinθcosθ Since x sinθ = y cosθ x sinθ (sin 2 θ + cos 2 θ) = s...

Please refer to the MCQ Questions for Class 10 Maths Trigonometry with Answers. The following Trigonometry Class 10 Maths MCQ Questions have been designed based on the current academic year syllabus and examination guidelines for Class 10. Our faculty has designed Trigonometry Class 10 MCQ Questions with Answers Please see below Trigonometry Class 10 Mathematics Question.If tan A= 3/4, then the value of sec A is 1v (a) 5/3 (b) 5/4 (c) 4/3 (d) 4/5 B Question. In the following questions, a statement of assertion (A) is followed by a statement reason (R). Choose the correct choice as: (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true. 1. Assertion (A): sin 267° + cos 267° = 1. Reason (R): For any value of q, sin 2θ + cos 2θ = 1. 2. Assertion (A): The value of sec 210° – cot 280° is 1. Reason (R): The value of sin 30° = 1/ 2 Related Posts: • Notes And Questions For NCERT Class 10 Mathematics… • MCQs for NCERT Class 10 Science Chapter 6 Life Processes • NCERT Solutions For Class 3 to 12 • MCQs For NCERT Class 11 Maths Trigonometric Functions With… • NCERT Books Download PDF Class 1 to 12 • Inverse Trigonometric Functions Class 12 Mathematics Exam…

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...

This class 10 Maths extra practice question is from chapter 8 - Introduction to Trigonometry. Concept Covered: Computing the value of angle by solving a trigonometric expression using Componendo Dividendo Rule. Level of difficulty: Hard Question 14: If θ is an acute angle and \\frac), find θ Explanatory Answer | Trigonometry Important Question 14 What is Componendo Dividendo Rule? If \\frac) ∴ sin θ = sin 60° θ = 60°