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Question: Answered & Verified by Expert
$\sqrt{2+\sqrt{2+2 \cos 4 \theta}}=$
MathematicsTrigonometric Ratios & IdentitiesMHT CETMHT CET 2020 (15 Oct Shift 2)
Options:
  • A $2 \cos \theta$
  • B $\frac{\cos \theta}{2}$
  • C $\frac{\cos \theta}{\sqrt{2}}$
  • D $\sqrt{2} \cdot \cos \theta$
Solution:
1177 Upvotes Verified Answer
The correct answer is: $2 \cos \theta$
$\begin{aligned} \sqrt{2+\sqrt{2+2 \cos 4 \theta}} &=\sqrt{2+\sqrt{2(1+\cos 4 \theta)}} \\ &=\sqrt{2+\sqrt{2 \times 2 \cos ^{2} 2 \theta}}=\sqrt{2+2 \cos ^{2} 2 \theta} \\ &=\sqrt{2\left(1+\cos ^{2} 2 \theta\right)}=\sqrt{2 \times 2 \cos ^{2} \theta}=2 \cos \theta \end{aligned}$

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