A) \[2{{\cos }^{2}}\theta \]
B) \[2\cos 2\theta \]
C) \[2\cos \theta \]
D) \[2\cos \frac{\theta }{2}\]
Correct Answer: C
Solution :
| \[\sqrt{2+\sqrt{2+2\cos 4\theta }}=\sqrt{2+\sqrt{2\,\,(1+\cos 4\theta )}}\] |
| \[=\sqrt{2+\sqrt{2\,\,(2{{\cos }^{2}}2\theta )}}\] |
| \[=\sqrt{2+\sqrt{4{{\cos }^{2}}2\theta }}\] |
| \[=\sqrt{2+2\cos 2\theta }=\sqrt{2\,\,(1+\cos 2\theta )}\] |
| \[=\sqrt{2\,\,(2{{\cos }^{2}}\theta )}=\sqrt{4{{\cos }^{2}}\theta }=2\cos \theta \] |
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