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AP EAMCET · Maths · Trigonometric Ratios & Identities

Minimum value of \(5 \tan ^2 \alpha+\frac{9}{\tan ^2 \alpha}+4 \sec ^2 \alpha\) is

  1. A \(24\)
  2. B \(22\)
  3. C \(32\)
  4. D \(28\)
Verified Solution

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 \(A M \geq G M\)…