2 sina cosb formula

2 Cos A Cos B is the product to sum trigonometric formulas that are used to rewrite the product of cosines into sum or difference. The 2 cos A cos B formula can help solve integration formulas involving the product of trigonometric ratio such as cosine. The formula of 2 Cos A Cos B can also be very helpful in simplifying the trigonometric expression by considering the product term such as Cos A Cos B and converting it into sum. Here, we will look at the 2 Cos A Cos B formula and how to derive the formula of 2 Cos A Cos B. 2 Cos A Cos B Formula Derivation The 2 Cos A Cos B formula can be derived by observing the sum and difference formula for cosine. As we know, • Cos ( A + B ) = Cos A Cos B - Sin A Sin B... (1) • Cos ( A- B ) = Cos A Cos B + Sin A Sin B…….(2) Adding the equation (1) and (2), we get Cos (A + B) + Cos (A - B) = Cos A Cos B - Sin A Sin B + Cos A Cos B + Sin A Sin B Cos (A + B) + Cos (A - B) = 2 Cos A Cos B (The term Sin A Sin B is cancelled due to the opposite sign). Therefore, the formula of 2 Cos A Cos B is given as: 2 Cos A Cos B = Cos (A + B) + Cos (A - B) In the above 2 Cos A Cos B formula, the left-hand side is the product of cosine whereas the right-hand side is the sum of the cosine. 2 Cos A Cos B Formula Application 1. Express 2 Cos 7x Cos 3y as a Sum Solution: Let A = 7x and B = 3y Using the formula: 2 Cos A Cos B = Cos (A + B) + Cos (A - B) Substituting the values of A and B in the above formula, we get 2 Cos A Cos B = Cos (7x + 3y) + Cos (7x - 3y)...

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``````````````````````````````````````````````````````````````````````````````````````````````````````````````````` Let us consider two unit • #hata-># inclined with positive direction of X-axis at angles A • # hat b-># inclined with positive direction of X-axis at angles 90-B, where # 90-B>A# • Angle between these two vectors becomes #theta=90-B-A=90-(A+B)#, #hata=cosAhati+sinAhatj# #hatb=cos(90-B)hati+sin(90-B)# #=sinBhati+cosBhatj# Now # hata xx hatb=(cosAhati+sinAhatj)xx(sinBhati+cosBhatj)# #=>|hata||hatb|sinthetahatk=cosAcosB(hatixxhatj)+sinAsinB(hatjxxhati)# Applying Properties of unit vectos #hati,hatj,hatk# #hatixxhatj=hatk # #hatjxxhati=-hatk # #hatixxhati= "null vector" # #hatjxxhatj= "null vector" # and #|hata|=1 and|hatb|=1" ""As both are unit vector" # Also inserting #theta=90-(A+B)#, Finally we get #=>sin(90-(A+B))hatk=cosAcosBhatk-sinAsinBhatk# #:.cos(A+B)=cosAcosB-sinAsinB# ``````````````````````````````````````````````````````````````````````````````````````````````````````` Sin(A+B) =SinA CosB + CosASinB formula can also be obtained by taking scalar product of #hata and hat b# Now # hata* hatb=(cosAhati+sinAhatj)*(sinBhati+cosBhatj)# #=>|hata||hatb|costheta=sinAcosB(hatj*hatj)+cosAsinB(hati*hati)# Applying Properties of unit vectos #hati,hatj,hatk# #hati*hatj=0 # #hatj*hati=0 # #hati*hati= 1 # #hatj*hatj= 1# and #|hata|=1 and|hatb|=1# Also inserting #theta=90-(A+B)#, Finally we get #=>cos(90-(A+B))=sinAcosB+cosAsinB# #:.sin(A+B)=sinAcosB+cosAsinB#

• • Menu Toggle • Application of Derivatives • Binomial Theorem • Circles • Complex Numbers • Continuity • Definite Integration • Determinants • Differentiability • Differential Equations • Differentiation • Ellipse • Function • Hyperbola • Indefinite Integration • Inverse Trigonometric Function • Limits • Logarithm • Matrices • Parabola • Permutation & Combination • Probability • Relation • Sequences & Series • Sets • Statistics • Straight Line • Trigonometric Equations • Trigonometry • Vectors • Menu Toggle • Circle • Ellipse • Function • Hyperbola • Integration • Inverse Trigonometric Function • Limit • Logarithm • Parabola • Permutation & Combination • Probability • Series • Sets • Statistics • Straight Line • Trigonometric Equations • Trigonometry • Vectors • Menu Toggle • Trigonometry • Trigonometric Equation • Straight Line • Statistics • Sets • Sequences and Series • Scalar and Vector • Relations • Probability • Permutation and Combination • Parabola • Logarithm • Limits • Inverse Trignometric Function • Integration • Differentiability • Hyperbola • Function • Ellipse • Circle • report this ad • • Menu Toggle • Application of Derivatives • Binomial Theorem • Circles • Complex Numbers • Continuity • Definite Integration • Determinants • Differentiability • Differential Equations • Differentiation • Ellipse • Function • Hyperbola • Indefinite Integration • Inverse Trigonometric Function • Limits • Logarithm • Matrices • Parabola • Permutation & Combination • Probabil...

2 Cos A Cos B is the product to sum trigonometric formulas that are used to rewrite the product of cosines into sum or difference. The 2 cos A cos B formula can help solve integration formulas involving the product of trigonometric ratio such as cosine. The formula of 2 Cos A Cos B can also be very helpful in simplifying the trigonometric expression by considering the product term such as Cos A Cos B and converting it into sum. Here, we will look at the 2 Cos A Cos B formula and how to derive the formula of 2 Cos A Cos B. 2 Cos A Cos B Formula Derivation The 2 Cos A Cos B formula can be derived by observing the sum and difference formula for cosine. As we know, • Cos ( A + B ) = Cos A Cos B - Sin A Sin B... (1) • Cos ( A- B ) = Cos A Cos B + Sin A Sin B…….(2) Adding the equation (1) and (2), we get Cos (A + B) + Cos (A - B) = Cos A Cos B - Sin A Sin B + Cos A Cos B + Sin A Sin B Cos (A + B) + Cos (A - B) = 2 Cos A Cos B (The term Sin A Sin B is cancelled due to the opposite sign). Therefore, the formula of 2 Cos A Cos B is given as: 2 Cos A Cos B = Cos (A + B) + Cos (A - B) In the above 2 Cos A Cos B formula, the left-hand side is the product of cosine whereas the right-hand side is the sum of the cosine. 2 Cos A Cos B Formula Application 1. Express 2 Cos 7x Cos 3y as a Sum Solution: Let A = 7x and B = 3y Using the formula: 2 Cos A Cos B = Cos (A + B) + Cos (A - B) Substituting the values of A and B in the above formula, we get 2 Cos A Cos B = Cos (7x + 3y) + Cos (7x - 3y)...

``````````````````````````````````````````````````````````````````````````````````````````````````````````````````` Let us consider two unit • #hata-># inclined with positive direction of X-axis at angles A • # hat b-># inclined with positive direction of X-axis at angles 90-B, where # 90-B>A# • Angle between these two vectors becomes #theta=90-B-A=90-(A+B)#, #hata=cosAhati+sinAhatj# #hatb=cos(90-B)hati+sin(90-B)# #=sinBhati+cosBhatj# Now # hata xx hatb=(cosAhati+sinAhatj)xx(sinBhati+cosBhatj)# #=>|hata||hatb|sinthetahatk=cosAcosB(hatixxhatj)+sinAsinB(hatjxxhati)# Applying Properties of unit vectos #hati,hatj,hatk# #hatixxhatj=hatk # #hatjxxhati=-hatk # #hatixxhati= "null vector" # #hatjxxhatj= "null vector" # and #|hata|=1 and|hatb|=1" ""As both are unit vector" # Also inserting #theta=90-(A+B)#, Finally we get #=>sin(90-(A+B))hatk=cosAcosBhatk-sinAsinBhatk# #:.cos(A+B)=cosAcosB-sinAsinB# ``````````````````````````````````````````````````````````````````````````````````````````````````````` Sin(A+B) =SinA CosB + CosASinB formula can also be obtained by taking scalar product of #hata and hat b# Now # hata* hatb=(cosAhati+sinAhatj)*(sinBhati+cosBhatj)# #=>|hata||hatb|costheta=sinAcosB(hatj*hatj)+cosAsinB(hati*hati)# Applying Properties of unit vectos #hati,hatj,hatk# #hati*hatj=0 # #hatj*hati=0 # #hati*hati= 1 # #hatj*hatj= 1# and #|hata|=1 and|hatb|=1# Also inserting #theta=90-(A+B)#, Finally we get #=>cos(90-(A+B))=sinAcosB+cosAsinB# #:.sin(A+B)=sinAcosB+cosAsinB#