AP EAMCET · Maths · Inverse Trigonometric Functions
If \(\frac{1}{2} \operatorname{Sin}^{-1}\left(\frac{3 \sin 2 \theta}{5+4 \cos 2 \theta}\right)=\operatorname{Tan}^{-1} x\) then \(x=\)
- A \(\tan \frac{\theta}{3}\)
- B \(\frac{1}{3} \tan \theta\)
- C \(\tan 3 \theta\)
- D \(\frac{1}{3} \tan 3 \theta\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{3} \tan \theta\)
Step-by-step Solution
Detailed explanation
\( \operatorname{Sin}^{-1}\left(\frac{3 \sin 2 \theta}{5+4 \cos 2 \theta}\right)=2 \operatorname{Tan}^{-1} x \) \( \frac{3 \sin 2 \theta}{5+4 \cos 2 \theta} = \frac{2x}{1+x^2} \)…
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