# The value of

Question:

The value of $\frac{1-\tan ^{2} 15^{\circ}}{2}$ is

(a) 1

(b) $\sqrt{3}$

(c) $\frac{\sqrt{3}}{2}$

(d) 2

Solution:

$\frac{1-\tan ^{2} 15^{\circ}}{1+\tan ^{2} 15^{\circ}}$

$\left[\right.$ Using identity : $\left.\frac{1-\tan ^{2} A}{1+\tan ^{2} A}=\cos 2 A\right]$

We have, $\frac{1-\tan ^{2} 15^{\circ}}{1+\tan ^{2} 15^{\circ}}=\cos 2\left(15^{\circ}\right)$

$=\cos 30^{\circ}$

$=\frac{\sqrt{3}}{2}$

Hence, the correct answer is option C.