AP EAMCET · Maths · Differentiation
Find the value of \(k\) if \(\frac{d}{d x}\left\{\frac{2}{\sqrt{2+\sqrt{2+\sqrt{2+2 \cos (4 x)}}}}\right\}\) \(=k \sec \left(\frac{x}{2}\right) \tan \left(\frac{x}{2}\right)\)
- A \(\frac{1}{2}\)
- B 2
- C 1
- D \(\frac{1}{8}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Let } y=\frac{2}{\sqrt{2+\sqrt{2+\sqrt{2+2 \cos 4 x}}}} \\ & \because \quad 1+\cos 2 A=2 \cos ^2 A \\ & \therefore y=\frac{2}{\sqrt{2+\sqrt{2+\sqrt{2(1+\cos 4 x)}}}} \\ & =\frac{2}{\sqrt{2+\sqrt{2+\sqrt{4 \cos ^2 2 x}}}}=\frac{2}{\sqrt{2+\sqrt{2+2 \cos…
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