Trigonometric Identities Question 287
Question: $ \frac{{{\cot }^{2}}15{}^\circ -1}{{{\cot }^{2}}15{}^\circ +1}= $
[MP PET 1998]
Options:
A) $ \frac{1}{2} $
B) $ \frac{\sqrt{3}}{2} $
C) $ \frac{3\sqrt{3}}{4} $
D) $ \sqrt{3} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \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} $ $ =\frac{{{\cos }^{2}}15^{o}-{{\sin }^{2}}15^{o}}{{{\cos }^{2}}15^{o}+{{\sin }^{2}}15^{o}}=\cos (30^{o})=\frac{\sqrt{3}}{2} $ .
BETA
