Question

If $\tan \theta =\frac{b}{a}$, then prove that $a\cos 2\theta +b\sin 2\theta =a$

Answer 1

$a\cos \theta +b\sin 2\theta$

$=a({\cos }^2\theta -{\sin }^2\theta )+b\left(2\sin \theta \cos \theta \right)$

$={\cos }^2\theta (a-a{\tan }^2\theta +2b\tan \theta )$

$=\frac{a-a{\tan }^2\theta +2b\tan \theta }{1+{\tan }^2\theta }$

$=a$