JEE Mains · Maths · STD 11 - 8. sequence and series
If the range of \(f(\theta)=\frac{\sin ^4 \theta+3 \cos ^2 \theta}{\sin ^4 \theta+\cos ^2 \theta}, \theta \in \mathbb{R}\) is \([\alpha, \beta]\), then the sum of the infinite \(G.P.\), whose first term is \(64\) and the common ratio is \(\frac{\alpha}{\beta}\), is equal to ...........
- A \(96\)
- B \(46\)
- C \(27\)
- D \(52\)
Answer & Solution
Correct Answer
(B) \(46\)
Step-by-step Solution
Detailed explanation
\( f(\theta)=\frac{\sin ^4 \theta+3 \cos ^2 \theta}{\sin ^4 \theta+\cos ^2 \theta} \) \( f(\theta)=1+\frac{2 \cos ^2 \theta}{\sin ^4 \theta+\cos ^2 \theta} \) \( f(\theta)=\frac{2 \cos ^2 \theta}{\cos ^4 \theta-\cos ^2 \theta+1}+1 \)…
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