Question

Prove that sin(3x)-sinx=2cos(2x)sinx ,
Hence solve for x if x E {-180;180}

Answer 1

We know that:\[\sin(p+q)=\sin(p)\cos(q)+\cos(p)\sin(q)\] and also know that\[\sin(p-q)=\sin(p)\cos(q)-\cos(p)\sin(q)\]Then:\[\sin(p+q)-\sin(p-q)=2\cos(p)\sin(q)\]And in our case (p+q)=3x and (p-q)=x ---->p=2x and q=x ---->sin(3x)-sin(x)=2cos(2x)sin(x)