JEE Mains · Maths · STD 11 - Trigonometrical equations
If the equation \(\cos ^{4} \theta+\sin ^{4} \theta+\lambda=0\) has real solutions for \(\theta,\) then \(\lambda\) lies in the interval
- A \(\left[-\frac{3}{2},-\frac{5}{4}\right]\)
- B \(\left(-\frac{1}{2},-\frac{1}{4}\right]\)
- C \(\left(-\frac{5}{4},-1\right)\)
- D \(\left[-1,-\frac{1}{2}\right]\)
Answer & Solution
Correct Answer
(D) \(\left[-1,-\frac{1}{2}\right]\)
Step-by-step Solution
Detailed explanation
\(\lambda=-\left(\sin ^{4} \theta+\cos ^{4} \theta\right)\) \(\lambda=-\left(\sin ^{2} \theta+\cos ^{2} \theta\right)^{2}-2 \sin ^{2} \theta \cos ^{2} \theta\) \(\lambda=\frac{\sin ^{2} 2 \theta}{2}-1\) \(\lambda \in\left[-1,-\frac{1}{2}\right]\)…
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