Question

Prove the identity sin3x=3sinx-4sin³x

Answer 1

Hi

we know that sin(A+B)=Sin(A)Cos(B)-Cos(A) Sin (B)

cos(2x)=1-2sin²(x)

sin(2x)=2sin(x)cos(x)

Exp:- Sin(3x)=Sin(x+2x)

Sin(x)cos(2x)+cos(x)sin(2x)

sin(x){1-2sin²(x)}+2cos²(x)sin(x)

sin(x)-2sin³(x)+2sin(x){1-sin²(x)}

sin(x)-2sin³(x)+2sin(x)-2sin³(x)

3sin(x)-4sin³(x)

Hope it helps....