cosa b costa b 2 c0sa cosb Prove the identity cosa b cos

cos(a b) + costa - b) 2 c0s(a) cos(b) Prove the identity. cos(a + b) + cos(a-b) = t (cos(a) costb) + sin(a) sin(b)) = cos(a) cos(b) + cos(a) cos(b) + sin(a) sin(b) Additional Materials eBook H Sum to Product Identities Sum to Product and Product 1n Sum Identities Example video points. 0SCAT19.4.2 Rewrite the sum as a praduct of two functions. Leave your answer in terms of sine and/or cosine cos(50°) +cos 16) Calculate this value numerically. (Round your answer to tour decimal places.) Additional Materials eBook Sum to Prodct Identies Sum to Product and Product to Sum Identities Learn by Example

Solution

cos (a + b) + cos ( a- b) = 2 cos a cos b

manipulating left hand side

cos ( a+ b ) + cos ( a- b ) = (cos a cos b - sin a sin b) + cos a cos b + sin a sin b

= cos a cos b + cos a cos b - sin a sin b + sin a sin b

= 2 cos a cos b

hence proved !