AP EAMCET · Maths · Trigonometric Ratios & Identities
Minimum value of \(5 \tan ^2 \alpha+\frac{9}{\tan ^2 \alpha}+4 \sec ^2 \alpha\) is
- A \(24\)
- B \(22\)
- C \(32\)
- D \(28\)
Answer & Solution
Correct Answer
(B) \(22\)
Step-by-step Solution
Detailed explanation
\(5 \tan ^2 \alpha+\frac{9}{\tan ^2 \alpha}+4 \sec ^2 \alpha\) \(=5 \tan ^2 \alpha+9 \cot ^2 \alpha+4\left(1+\tan ^2 \alpha\right)\) \(\left[\because \sec ^2 x=1+\tan ^2 x\right]\) \(=9 \tan ^2 \alpha+9 \cot ^2 \alpha+4\) Since, we know that \(A M \geq G M\)…
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