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AP EAMCET · Maths · Trigonometric Equations

If \(3 \sin ^4 x+2 \cos ^4 x=\frac{6}{5}\) and \(x\) is an acute angle, then \(\tan 2 \mathrm{x}=\)

  1. A \(\frac{2 \sqrt{6}}{5}\)
  2. B \(2 \sqrt{6}\)
  3. C \(\frac{3 \sqrt{2}}{5}\)
  4. D \(\frac{2 \sqrt{3}}{5}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(2 \sqrt{6}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text {} \because 3 \sin ^4 x+2 \cos ^4 x=\frac{6}{5} \\ & \Rightarrow 3 \sin ^4 x+2\left(1-\sin ^2 x\right)^2=\frac{6}{5} \\ & \Rightarrow 3 \sin ^4 x+2\left(1+\sin ^4 x-2 \sin ^2 x\right)=\frac{6}{5} \\ & \Rightarrow 25 \sin ^4 x-20 \sin ^2 x+4=0 \\ &…