JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
The value of \(\tan \left(2 \tan ^{-1}\left(\frac{3}{5}\right)+\sin ^{-1}\left(\frac{5}{13}\right)\right)\) is equal to:
- A \(\frac{-291}{76}\)
- B \(\frac{-181}{69}\)
- C \(\frac{151}{63}\)
- D \(\frac{220}{21}\)
Answer & Solution
Correct Answer
(D) \(\frac{220}{21}\)
Step-by-step Solution
Detailed explanation
\(\underbrace{\tan ^{-1} \frac{3}{5}+\tan ^{-1} \frac{3}{5}}_{\times\,>\,0, y\,>\,0, x y\,<\,1}+\tan ^{-1} \frac{5}{12}\) \(\tan ^{-1} \frac{\frac{6}{5}}{1-\frac{9}{25}}=\underbrace{\tan ^{-1} \frac{15}{8}+\tan ^{-1} \frac{5}{12}}_{x\,>\,0, y\,>\,0, x y\,<\,1}\)…
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