Question

Sin3x

Answer 1

sin(3x)
= sin(2x+x)
= sin(2x)cos(x) + cos(2x)sin(x)
= (2 sin(x)cos(x)) cos(x) + (1 - 2sin²x) sin(x)
= 2 sin(x)cos²x + sin(x) - 2sin³x
= 2 sin(x) (1-sin²x) + sin(x) - 2sin³x
= 2 sin(x) - 2sin³x + sin(x) - 2sin³x
= 3 sin(x) - 4 sin³x