JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
The sum of all values of \(\theta \, \in \,\left( {0,\frac{\pi }{2}} \right)\) satisfying \({\sin ^2}\,2\theta + {\cos ^4}\,2\theta = \frac{3}{4}\) is
- A \(\pi \)
- B \(\frac{{5\pi }}{4}\)
- C \(\frac{{\pi }}{2}\)
- D \(\frac{{3\pi }}{8}\)
Answer & Solution
Correct Answer
(C) \(\frac{{\pi }}{2}\)
Step-by-step Solution
Detailed explanation
\({\sin ^2}2\theta \, + \,{\cos ^4}2\theta \, = \frac{3}{4}\) Let \(\,{\cos ^2}2\theta \, =t \) \( \Rightarrow \,1\, - \,\,{\cos ^2}2\theta \, + \,{\cos ^4}2\theta \, = \frac{3}{4}\) \( \Rightarrow t = \frac{1}{2}\, \Rightarrow \,\,{\cos ^2}2\theta \, = \frac{1}{2}\,\)…
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