Question

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

Answer 1

= 2sin 9x cos 2x

Using,

sin(A + B) = sinA cosB + cosA sinB

= 2cos\(\frac{10x}{2}sin\frac{4x}{2}\)

= 2cos5x sin2x

Using,

sin( A - B)= sinA cos B - cosA sinB

= \(2cos\frac{12x}{2}cos\frac{2x}{2}\)

= 2cos 6x cosx

Using,

cos (A + B) = cosAcosB - sinAsinB

= -2sin\(\frac{6x}{2}\)sin\(\frac{-2x}{2}\)

= 2sin3x sinx

Using,

cos (A - B) = cosAcosB + sinAsinB