WBJEE · Maths · Functions
If \(\mathrm{P}=\frac{1}{2} \sin ^2 \theta+\frac{1}{3} \cos ^2 \theta\) then
- A \(\frac{1}{3} \leq \mathrm{P} \leq \frac{1}{2}\)
- B \(\mathrm{P} \geq \frac{1}{2}\)
- C \(\quad 2 \leq \mathrm{P} \leq 3\)
- D \(-\frac{\sqrt{13}}{6} \leq \mathrm{P} \leq \frac{\sqrt{13}}{6}\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{3} \leq \mathrm{P} \leq \frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Hints: \(P=\frac{1}{2} \sin ^2 \theta+\frac{1}{3} \cos ^2 \theta=\frac{1}{2} \sin ^2 \theta+\frac{1}{3}\left(1-\sin ^2 \theta\right)=\frac{1}{3}+\frac{1}{6} \sin ^2 \theta\)…
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