^2 15^ -1 ^2 15^ +1 = - Vidyadip

MCQ

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

A
$\frac{1}{2}$
✓
$\frac{\sqrt{3}}{2}$
C
$\frac{3 \sqrt{3}}{4}$
D
$\sqrt{3}$

✓

Answer

Correct option: B.

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

(B)
$\frac{\cot ^2 15^{\circ}-1}{\cot ^2 15^{\circ}+1}=\frac{\frac{\cos ^2 15^{\circ}}{\sin ^2 15^{\circ}}-1}{\frac{\cos ^2 15^{\circ}}{\sin ^2 15^{\circ}}+1}$
$=\frac{\cos ^2 15^{\circ}-\sin ^2 15^{\circ}}{\cos ^2 15^{\circ}+\sin ^2 15^{\circ}}=\cos \left(30^{\circ}\right)$
$\left[\because \cos ^2 A-\sin ^2 B=\cos (A+B) \cos (A-B)\right]$
$=\frac{\sqrt{3}}{2}$

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