Trigonometric Identities Question 344
Question: The value of $ \tan 7\frac{1}{2}{}^\circ $ is equal to
[J & K 2005]
Options:
A) $ \sqrt{6}+\sqrt{3}+\sqrt{2}-2 $
B) $ \sqrt{6}-\sqrt{3}+\sqrt{2}-2 $
C) $ \sqrt{6}-\sqrt{3}+\sqrt{2}+2 $
D) $ \sqrt{6}-\sqrt{3}-\sqrt{2}-2 $
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ \tan A=\frac{\sin A}{\cos A}=\frac{2\sin A\cos A}{2{{\cos }^{2}}A}=\frac{\sin 2A}{1+{{\cos }^{2}}A} $ Putting $ A=7{{\frac{1}{2}}^{o}}\Rightarrow \tan 7{{\frac{1}{2}}^{o}}=\frac{\sin 15^{o}}{1+\cos 15^{o}} $ On simplification, we get $ \tan 7{{\frac{1}{2}}^{o}}=\sqrt{6}-\sqrt{3}+\sqrt{2}-2 $ .
BETA
