Question

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

Answer 1

Answer:

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