MHT CET · Maths · Trigonometric Ratios & Identities
\(\sqrt{2+\sqrt{2+2 \cos 4 \theta}}=\)
- A \(2 \cos \theta\)
- B \(\frac{\cos \theta}{2}\)
- C \(\frac{\cos \theta}{\sqrt{2}}\)
- D \(\sqrt{2} \cdot \cos \theta\)
Answer & Solution
Correct Answer
(A) \(2 \cos \theta\)
Step-by-step Solution
Detailed explanation
\(\sqrt{2+\sqrt{2+2 \cos 4 \theta}} =\sqrt{2+\sqrt{2(1+\cos 4 \theta)}} \)
\( =\sqrt{2+\sqrt{2 \times 2 \cos ^{2} 2 \theta}}=\sqrt{2+2 \cos ^{2} 2 \theta} \)
\( =\sqrt{2\left(1+\cos ^{2} 2 \theta\right)}=\sqrt{2 \times 2 \cos ^{2} \theta}=2 \cos \theta\)
\( =\sqrt{2+\sqrt{2 \times 2 \cos ^{2} 2 \theta}}=\sqrt{2+2 \cos ^{2} 2 \theta} \)
\( =\sqrt{2\left(1+\cos ^{2} 2 \theta\right)}=\sqrt{2 \times 2 \cos ^{2} \theta}=2 \cos \theta\)
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