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.