How do you prove $1-cos5thetacos3theta-sin5thetasin3theta=2sin^2theta$ ?

Question

1736 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-20T11:38:56

We use the identity $cos2theta=1-2sin^2theta$ and $cos(A-B)=cosAcosB+sinAsinB$

We know that $cos2theta=1-2sin^2theta$

But as $2theta=5theta-3theta$ , we have

$cos(5theta-3theta)=1-2sin^2theta$

or $cos5thetacos3theta+sin5thetasin3theta=1-2sin^2theta$

or $1-cos5thetacos3theta-sin5thetasin3theta=2sin^2theta$

How do you prove 1-cos5thetacos3theta-sin5thetasin3theta=2sin^2theta1-cos5thetacos3theta-sin5thetasin3theta=2sin^2theta?