Question

$\frac{\sin x}{a}=\frac{\cos x}{b}$, prove that a $\sin 2x+b\cos 2x=b.$

Answer 1

$a\sin 2x+b\cos 2x=2a\sin x\cos x+b({\cos }^{2}x-{\sin }^{2}x)$

Since $a\cos x=b\sin x$

above equation becomes $2\sin x\left(b\sin x\right)+b({\cos }^{2}x-{\sin }^{2}x)=b({\cos }^{2}x+{\sin }^{2}x)=b$