Question:
If \( \sin \left(\sin^{-1} \frac{1}{5} + \cos^{-1} x\right) = 1 \), then the value of \( x \) is
If \( \sin \left(\sin^{-1} \frac{1}{5} + \cos^{-1} x\right) = 1 \), then the value of \( x \) is
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Identity: $\sin^{-1}x + \cos^{-1}x = \pi/2$.
Updated On: May 12, 2026
- \( \frac{1}{5} \)
- 1
- 0
- \( -\frac{1}{5} \)
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Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Concept
$\sin \theta = 1$ implies $\theta = \pi/2$ (for principal values).
Step 2: Meaning
$\sin^{-1} (1/5) + \cos^{-1} x = \sin^{-1} 1 = \pi/2$.
Step 3: Analysis
We know the identity $\sin^{-1} A + \cos^{-1} A = \pi/2$ for all $|A| \le 1$.
Step 4: Conclusion
By comparing $\sin^{-1} (1/5) + \cos^{-1} x = \pi/2$ with the identity, we get $x = 1/5$. Final Answer: (A)
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