A) \[\cos 2\theta \]
B) \[\cos 3\theta \]
C) \[\sin 2\theta \]
D) \[\sin 3\theta \]
Correct Answer: A
Solution :
We have,\[\cos 2(\theta +\varphi )-4\cos (\theta +\varphi )\sin \theta \sin \varphi +2{{\sin }^{2}}\varphi \] Now, put \[\theta =\varphi =\frac{\pi }{4}\] \[\cos 2\left( \frac{\pi }{2} \right)-4\cos \left( \frac{\pi }{2} \right)\sin \left( \frac{\pi }{4} \right)\sin \left( \frac{\pi }{4} \right)+2{{\sin }^{2}}\left( \frac{2\pi }{4} \right)=0\] Put \[\theta =\varphi =\pi /4\] in option (a), Then, \[\cos 2\theta =\cos \pi /2=0\]. Hence option (a) is correct.
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