Question:
If $4 \sin^{-1} x + \cos^{-1} x = \pi$ then $x =$
If $4 \sin^{-1} x + \cos^{-1} x = \pi$ then $x =$
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Use identity $\sin^{-1}x + \cos^{-1}x = \frac{\pi}{2}$.
Updated On: Apr 26, 2026
- $\frac{\sqrt{3}}{2}$
- 0
- $\frac{1}{2}$
- $\frac{1}{\sqrt{2}}$
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The Correct Option is C
Solution and Explanation
Concept:
\[ \sin^{-1}x + \cos^{-1}x = \frac{\pi}{2} \] Step 1: Substitute. \[ 4\sin^{-1}x + \left(\frac{\pi}{2}-\sin^{-1}x\right)=\pi \]
Step 2: Simplify. \[ 3\sin^{-1}x = \frac{\pi}{2} \Rightarrow \sin^{-1}x = \frac{\pi}{6} \]
Step 3: Find x. \[ x = \frac{1}{2} \] Conclusion. Answer = $\frac{1}{2}$
\[ \sin^{-1}x + \cos^{-1}x = \frac{\pi}{2} \] Step 1: Substitute. \[ 4\sin^{-1}x + \left(\frac{\pi}{2}-\sin^{-1}x\right)=\pi \]
Step 2: Simplify. \[ 3\sin^{-1}x = \frac{\pi}{2} \Rightarrow \sin^{-1}x = \frac{\pi}{6} \]
Step 3: Find x. \[ x = \frac{1}{2} \] Conclusion. Answer = $\frac{1}{2}$
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