Question

If A = 60⁰ and B = 30⁰, verify that: 

(ii) cos (A – B) = cos A cos B + sin A sin B

Answer 1

cos (A – B) = cos 30^{0 =}`sqrt(3)/2`

cos A cos B + sin A sin B = cos 60⁰ cos 30⁰ + sin 60⁰ sin 30⁰ 

⁼`( 1/2 xx sqrt(3)/2 + sqrt(3)/2 xx1/2) = (sqrt(3)/4 + sqrt(3)/4) = 2 xx sqrt(3)/4 = sqrt(3)/2`

∴ cos (A – B) = cos A cos B + sin A sin B