Solve $\sin^{-1}(x) \cos^{-1}(x) = -1$

Question

I only managed to write the equation in the following form:

$sin^{-1}(x)sin^{-1}\sqrt{1-x^2} = -1$

I'm not sure where to go from here :(

Thanks in advance!

PS: The answer is $-0.47$ (correct to 2 decimal places)

Answer 1

If $t=\sin^{-1}x, -\dfrac\pi2\le t\le-\dfrac\pi2\ \ \ \ (1)$

$$-1=t\left(\dfrac\pi2-t\right)$$

$$\iff2t^2-\pi t-2=0$$

Check which value of $t$ satisfies $(1)$