Question

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

Identities.
A. 8sin(x) cos(x) - 4 sin(x) cos(x)
B. 8sin(x) cos(x)
C. 8sin(x) cos(x) – 8 sin(x) cos(x)
D. 8 sin(x) cos' (x) +8sin(x) cos(x)

Answer 1

`{ \bf{ = \sin(4x) + 2 \sin(2x) }} \\ = { \bf{2 \sin(2x) \cos(2x) + 4 \sin(x) \cos(x) }} \\ { \bf{ = 4 \sin(x) \cos(x) . ({ \cos }^(2) x - { \sin}^(2) }x) + 4 \sin(x) \cos(x) } \\ = { \bf{4 \sin(x) \cos(x) ( { \cos }^(2)x - { \sin }^(2)x + 1) }} \\ = { \bf{4 \sin(x) \cos(x) }(2 { \cos }^(2) x)} \\ = { \bf{8 \sin(x) { \cos}^(3)x }}`