Prove that

Express each of the following as a product.

1. sin 10x + sin 6x

2. sin 7x – sin 3x

3. cos 7x + cos 5x

4. cos2x – cos 4x

Express each of the following as an algebraic sum of sines or cosines :

(i) 2sin 6x cos 4x

(ii) 2cos 5x din 3x

(iii) 2cos 7x cos 3x

(iv) 2sin 8x sin 2x

Prove that

Prove that