How do you verify $costheta(1-4sin^2theta)=costhetacos(2theta)-sinthetasin(2theta)$ ?

Question

1896 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-21T19:09:14

see below

$cos theta(1-4sin^2 theta)=cos theta cos2 theta-sin theta sin 2 theta$

Use the formulas : $cos 2 theta=1-2sin^2 theta, sin 2theta=2sinthetacos theta$

Right Side : $=cos theta cos2 theta-sin theta sin 2 theta$

$=cos theta (1-2sin^2theta)-sin theta*2sin theta cos theta$

$=cos theta (1-2sin^2theta-2sin^2theta)$

$=cos theta(1-4sin^2 theta)$

$:.=$ Left Side

How do you verify costheta(1-4sin^2theta)=costhetacos(2theta)-sinthetasin(2theta)costheta(1-4sin^2theta)=costhetacos(2theta)-sinthetasin(2theta)?