If 4sin−1⁡x+cos−1⁡x=π then x equal

# If $4{\mathrm{sin}}^{-1}x+{\mathrm{cos}}^{-1}x=\pi$ then $x$ equal

1. A

$\frac{1}{2}$

2. B

$\frac{\sqrt{3}}{2}$

3. C

$-\frac{1}{2}$

4. D

none of these

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### Solution:

We have,

$\begin{array}{l}4{\mathrm{sin}}^{-1}x+{\mathrm{cos}}^{-1}x=\pi \\ ⇒4{\mathrm{sin}}^{-1}x+\frac{\pi }{2}-{\mathrm{sin}}^{-1}x=\pi \\ ⇒3{\mathrm{sin}}^{-1}x=\frac{\pi }{2}⇒x=\mathrm{sin}\left(\frac{\pi }{6}\right)=\frac{1}{2}\end{array}$

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