AP EAMCET · Maths · Trigonometric Ratios & Identities
The range of \(\frac{1}{\sin ^2 x+3 \sin x \cos x+5 \cos ^2 x}\) is
- A \(\left[2, \frac{11}{2}\right]\)
- B \(\left[\frac{1}{2}, \frac{11}{2}\right]\)
- C \(\left[\frac{2}{11}, \frac{1}{2}\right]\)
- D \(\left[\frac{2}{11}, 2\right]\)
Answer & Solution
Correct Answer
(D) \(\left[\frac{2}{11}, 2\right]\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text {Let } f(x)=\frac{1}{\sin ^2 x+3 \sin x \cos x+5 \cos ^2 x} \\ & \text { let, } g(x)=\sin ^2 x+3 \sin x \cos x+5 \cos ^2 x \\ & =2[1+\cos 2 \theta]+1+\frac{3}{2} \sin 2 \theta \\ & g(x)=\frac{3}{2} \sin 2 \theta+2 \cos 2 \theta+3\end{aligned}\) We know…
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