JEE Mains · Maths · STD 12 - 2. inverse trigonometric function
If \(\sin ^{-1} \frac{\alpha}{17}+\cos ^{-1} \frac{4}{5}-\tan ^{-1} \frac{77}{36}=0,0 < \alpha < 13\), then \(\sin ^{-1}(\sin \alpha)+\cos ^{-1}(\cos \alpha)\) is equal to \(.........\).
- A \(\pi\)
- B \(16\)
- C \(0\)
- D \(16-5\,\pi\)
Answer & Solution
Correct Answer
(A) \(\pi\)
Step-by-step Solution
Detailed explanation
\(\cos ^{-1} \frac{4}{5}=\tan ^{-1} \frac{3}{4}\) \(\therefore \sin ^{-1} \frac{\alpha}{17}=\tan ^{-1} \frac{77}{36}-\tan ^{-1} \frac{3}{4}=\tan ^{-1}\left(\frac{\frac{77}{36}-\frac{3}{4}}{1+\frac{77}{36} \cdot \frac{3}{4}}\right)\)…
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