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Question: \[\frac{\cot^{2}15{^\circ} - 1}{\cot^{2}15{^\circ} + 1} =\]...

cot⁡215∘−1cot⁡215∘+1=\frac{\cot^{2}15{^\circ} - 1}{\cot^{2}15{^\circ} + 1} =

A

12\frac{1}{2}

B

32\frac{\sqrt{3}}{2}

C

334\frac{3\sqrt{3}}{4}

D

3\sqrt{3}

Answer

32\frac{\sqrt{3}}{2}

Explanation

Solution

cot⁡215o−1cot⁡215o+1=cos⁡215osin⁡215o−1cos⁡215osin⁡215o+1\frac{\cot^{2}15^{o} - 1}{\cot^{2}15^{o} + 1} = \frac{\frac{\cos^{2}15^{o}}{\sin^{2}15^{o}} - 1}{\frac{\cos^{2}15^{o}}{\sin^{2}15^{o}} + 1}

=cos⁡215o−sin⁡215ocos⁡215o+sin⁡215o=cos⁡(30o)=32= \frac{\cos^{2}15^{o} - \sin^{2}15^{o}}{\cos^{2}15^{o} + \sin^{2}15^{o}} = \cos(30^{o}) = \frac{\sqrt{3}}{2}.