Value of $x$ in $\sin^{-1}(x)+\sin^{-1}(1-x)=\cos^{-1}(x)$ How can we find the value of $x$ in $\sin^{-1}(x)+\sin^{-1}(1-x)=\cos^{-1}(x)$? 
Note that $\sin^{-1}$ is the inverse sine function.
I'm asking for the solution $x$ for this equation.
Please work out the solution.

An alternative approach would be to take the cosine of both sides of the equation and then use the compound angle formula for $\cos(A+B)$. This leads to the equation $$\sqrt{1-x^2}\sqrt{1-(1-x^2)}-x(1-x)=x$$
This simplifies quote nicely and you get the same answers as have already been found, i.e. $x=0$ and $x=\frac 12$
