Trigonometric Identities Question 168

Question: $ \tan 15{}^\circ = $

[EAMCET 1981]

Options:

A) $ \frac{1}{3} $

B) $ \sqrt{3}-2 $

C) $ 2-\sqrt{3} $

D) None of these

Show Answer

Answer:

Correct Answer: C

Solution:

$ \tan 15^{o}=\tan (45^{o}-30^{o}) $ $ =\frac{1-1/\sqrt{3}}{1+1/\sqrt{3}}=\frac{\sqrt{3}-1}{\sqrt{3}+1}\times \frac{\sqrt{3}-1}{\sqrt{3}-1}=2-\sqrt{3} $ .