Power Reducing Formula

Question

Use the power reducing formula on sin^3(x)

Answer 1

As sin(x) = 1/2i(e^ix-e^-ix), sin³(x) = (1/2i(e^ix-e^-ix))³ =

-1/8i(e^3ix -3e^ix + 3e^-ix -e^-3ix) =

-1/4(1/2i(e^3ix -e^-3ix)) + 3/4(1/2i(e^ix-e^-ix)) =

-1/4 sin(3x) + 3/4 sin(x)