Express each of the following as an algebraic sum of sines or cosines : (i) 2sin 6x cos 4x (ii) 2cos 5x din 3x

Answer:

i) 2sin 6x cos 4x = sin (6x+4x) + sin (6x-4x)
= sin 10x + sin 2x
Using,
2sinAcosB = sin (A+ B) + sin (A – B)

ii) 2cos 5x sin3x = sin (5x + 3x) – sin (5x – 3x)
= sin8x – sin2x
Using,
2cosAsinB = sin(A + B) – sin (A – B)