Question

Simplify the trigonometric expression sin(4x) +2 sin(2x) using Double-Angle
Identities.

Answer 1

8sin(x)cos³(x)

Explanation:

sin(4x) +2 sin(2x) = 2sin(2x)*cos(2x) + 2sin(2x) = 2sin(2x)(cos2x + 1)=

= 2sin(2x)(cos²x - sin²x + cos²x + sin²x)=²2sin(2x)*(2cos²x)=

= 4*2sin(x)*cos(x)*cos²(x)= 8sin(x)cos³(x)