Question

Show that `Sin3theta= 3sin theta–4sin³theta` ?

Answer 1

We have that

`sin(3theta)=sin(2theta+theta)=sin(2theta)*cos(theta)+cos(2theta)*sin(theta)=2sintheta*cos^2theta+sintheta*(1-2sin^2theta)=2*sintheta*(1-sin^2theta)+sintheta*(1-2sin^2theta)=3*sintheta-4sin^3theta`

We used the following trigonometric identities

`sin(x+y)=sinx*cosy+cosx*siny`

`sin(2x)=2sinx*cosx`

`cos(2x)=1-2sin^2x`

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