sin (a + b) = sin a cos b + sin b cos a sin(a - b) = sin a cos b - sin b cos a and cos(a + b) = cos a cos b - sin a sin b cos(a - b) = cos a cos b + sin a sin b. (a) From those four, obtain the...

sin (a + b) = sin a cos b + sin b cos a sin(a - b) = sin a cos b - sin b cos a and cos(a + b) = cos a cos b - sin a sin b cos(a - b) = cos a cos b + sin a sin b. (a) From those four, obtain the identity that we used, namely, sin A cos B = 1/2 [Sin (A - B) + Sin (A + B)] (b) Also from those four, obtain the "companion identities" sin A sin B = 1/2 [cos (A - B) - cos(A + B)], cos A cos B = 1/2 [cos (A + B) + cos(A - B)]