COMEDK · Maths · 23. Inverse Trigonometric Functions
If \(\sin ^{-1} \frac{x}{5}+\operatorname{cosec}^{-1} \frac{5}{4}=\frac{\pi}{2}\), then \(x\) is equal to
- A \(1\)
- B \(4\)
- C \(3\)
- D \(5\)
Answer & Solution
Correct Answer
(C) \(3\)
Step-by-step Solution
Detailed explanation
We have, \(\sin ^{-1} \frac{x}{5}+\operatorname{cosec}^{-1} \frac{5}{4}=\frac{\pi}{2}\) \(\Rightarrow \quad \sin ^{-1} \frac{x}{5}+\sin ^{-1} \frac{4}{5}=\frac{\pi}{2}\) \(\Rightarrow \quad \sin ^{-1} \frac{x}{5}+\cos ^{-1} \frac{3}{5}=\frac{\pi}{2}\)…
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