Trigonometric Identities Question 325
Question: $ \cos 2(\theta +\varphi )-4\cos (\theta +\varphi )\sin \theta \sin \varphi +2{{\sin }^{2}}\varphi = $
[Orissa JEE 2004]
Options:
A) $ \cos 2\theta $
B) $ \cos 3\theta $
C) $ \sin 2\theta $
D) $ \sin 3\theta $
Show Answer
Answer:
Correct Answer: A
Solution:
We have, $ \cos 2(\theta +\varphi )-4\cos (\theta +\varphi )\sin \theta \sin \varphi +2{{\sin }^{2}}\varphi $ Now, put $ \theta =\varphi =\frac{\pi }{4} $ $ \cos 2( \frac{\pi }{2} )-4\cos ( \frac{\pi }{2} )\sin ( \frac{\pi }{4} )\sin ( \frac{\pi }{4} )+2{{\sin }^{2}}( \frac{2\pi }{4} )=0 $ Put $ \theta =\varphi =\pi /4 $ in option (a), Then, $ \cos 2\theta =\cos \pi /2=0 $ . Hence option (a) is correct.
BETA
