Question

If $4si{n}^{-1}x+co{s}^{-1}x=\pi$ then x is equal to

• A. -1/2
• B. 0
• C. 1/2
• D. 1

Answer 1

The correct option is C

1/2

$4si{n}^{-1}x+co{s}^{-1}x=\pi$
$\Rightarrow 4si{n}^{-1}x+(\frac{\pi }{2}-si{n}^{-1}x)=\pi$
$\Rightarrow 3si{n}^{-1}x=\pi -\frac{\pi }{2}=\frac{\pi }{2}$
$\Rightarrow si{n}^{-1}x=\frac{\pi }{6}$
$\Rightarrow x=sin\frac{\pi }{6}=\frac{1}{2}$