Prove that:
Question:

Prove that:

$\sqrt{\frac{1-\cos 2 x}{1+\cos 2 x}}=\tan x$

Solution:

$\mathrm{LHS}=\sqrt{\frac{1-\cos 2 x}{1+\cos 2 x}}$

$=\sqrt{\frac{2 \sin ^{2} x}{2 \cos ^{2} x}} \quad\left[\because 1-\cos 2 x=2 \sin ^{2} x\right.$ and $\left.1+\cos 2 x=2 \cos ^{2} x\right]$

$=\frac{\sin x}{\cos x}$

$=\tan x=\mathrm{RHS}$

Hence proved.

Administrator

Leave a comment

Please enter comment.
Please enter your name.