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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

  1. A \(1\)
  2. B \(4\)
  3. C \(3\)
  4. D \(5\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(3\)

Step-by-step Solution

Detailed explanation

We have, \(\sin ^{-1} \frac{x}{5}+\operatorname{cosec}^{-1} \frac{5}{4}=\frac{\pi}{2}\) \(\Rightarrow \quad \sin ^{-1} \frac{x}{5}+\sin ^{-1} \frac{4}{5}=\frac{\pi}{2}\) \(\Rightarrow \quad \sin ^{-1} \frac{x}{5}+\cos ^{-1} \frac{3}{5}=\frac{\pi}{2}\)…