Use the producttosum or sumtoproduct identities to find an i

Use the product-to-sum or sum-to-product identities to find an identity for the given expression, sin 32 degree cos 41 degree A. 2(sin 73 degree - sin 9 degree) B. 1/2(sin 9 degree - sin 9 degree) c. 1/2(cos 73 degree + sin 9 degree) D. 1/2 (sin 73 degree - sin 9 degree)

Solution

As   sin A cos B = (1/2)* (sin(A + B) + sin(A B))

sin32*cos41 = (1/2)*[sin(32 + 41) + sin(32 - 41)]

= (1/2)*[sin 73 + sin(-9)]

= (1/2)*[sin 73 - sin(9)]