WBJEE · Maths · Trigonometric Ratios & Identities
Simplest form of \(\frac{2}{\sqrt{2+\sqrt{2+\sqrt{2+2 \cos 4 x}}}}\) is
- A \(\sec \frac{x}{2}\)
- B \(\sec x\)
- C \(\operatorname{cosec} x\)
- D 1
Answer & Solution
Correct Answer
(A) \(\sec \frac{x}{2}\)
Step-by-step Solution
Detailed explanation
\[ \text { Hints : } \begin{aligned} & \frac{2}{\sqrt{2+\sqrt{2+\sqrt{2.2 \cos ^2 2 x}}}}=\frac{2}{\sqrt{2+\sqrt{2+2 \cos 2 x}}}=\frac{2}{\sqrt{2+\sqrt{2.2 \cos ^2 x}}} \\ & =\frac{2}{\sqrt{2+2 \cos x}}=\frac{2}{2 \cos \frac{x}{2}}=\sec \frac{x}{2} \end{aligned} \]
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