JEE Mains · Maths · STD 11 - Trigonometrical equations
The set of all values of \(\lambda\) for which the equation \(\cos ^2 2 x-2 \sin ^4 x-2 \cos ^2 x=\lambda\)
- A \([-2,-1]\)
- B \(\left[-2,-\frac{3}{2}\right]\)
- C \(\left[-1,-\frac{1}{2}\right]\)
- D \(\left[-\frac{3}{2},-1\right]\)
Answer & Solution
Correct Answer
(D) \(\left[-\frac{3}{2},-1\right]\)
Step-by-step Solution
Detailed explanation
\(\lambda=\cos ^2 2 x-2 \sin ^4 x-2 \cos ^2 x\) \(\text { convert all in to } \cos x \text {. }\) \(\lambda=\left(2 \cos ^2 x-1\right)^2-2\left(1-\cos ^2 x\right)^2-2 \cos ^2 x\) \(=4 \cos ^4 x-4 \cos ^2 x+1-2\left(1-2 \cos ^2 x+\cos ^4 x\right)-\) \(2 \cos ^2 x\)…
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