Trigonometric Identities Question 179
Question: If $ \tan \alpha =\frac{1}{7},\ \tan \beta =\frac{1}{3}, $ then $ \cos 2\alpha = $
[CET 1986]
Options:
A) $ \sin 2\beta $
B) $ \sin 4\beta $
C) $ \sin 3\beta $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \cos 2\alpha =\frac{1-t^{2}}{1+t^{2}}=\frac{24}{25} $ {Here $ t=\tan \alpha $ } $ \sin 2\beta =\frac{2T}{1+T^{2}}=\frac{3}{5}\Rightarrow \cos 2\beta =\frac{4}{5} $ { $ T=\tan \beta $ }
$ \therefore \sin 4\beta =2\sin 2\beta \cos 2\beta =2.\frac{3}{5}.\frac{4}{5}=\frac{24}{25}=\cos 2\alpha $ .
BETA
