Question

If $4si{n}^{-1}x+co{s}^{-1}x=\pi ,$ then find the value of x.

Answer 1

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