Express the product as a sum containing only sin or cosines

Express the product as a sum containing only sin or cosines. 7) sin (90) cos (50) Express the sum or difference as a product of sines and/or cosines. 8 sin (100) sin (40)

Solution

sin 10 theta + sin 4 theta

sin A + sin B= 2 sin(A+B)/2 cos (A-B)/2

THerefore sin 10 theta + sin 4 theta= 2sin(10 theta + 4theta)/2 cos (10 theta-4 theta)/2

                                                        =2sin 7theta cos 3theta