Question

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

Answer 1

Given $\tan x=\frac{b}{a}$......(1).

Now

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

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

$=a.\frac{a^2-b^2}{a^2+b^2}+b.\frac{2ab}{a^2+b^2}$ [ Using (1)]

$=\frac{a(a^2+b^2)}{a^2+b^2}$

$=a$.