Question

Question #fa8db

Answer 1

See Below

Explanation:

`sin (3x)=3sin x-4sin^3 x`

Use the formulas
`sin (A+B) = sin A cos B + cos A sin B`

`sin 2A = 2sin A cos A`

`cos 2A = 1- 2 sin ^ 2 A`

Left Side: `sin 3x=sin(2x+x)=sin2xcosx+cos2xsin x`

`=2sinx cosx cosx + (1-2sin^2 x)sin x`

`=2sinx cos^2 x+ sinx-2sin^3 x`

`=2sinx(1-sin^2 x) + sinx-2 sin^3 x`

`=2 sin x-2sin^3 x + sin x -2 sin^3 x`

`=3 sin x -4 sin^ 3 x`

`=` Right Side