Answer
True.
Work Step by Step
The derivative of a function $f(x) = sin^{-1}(x)+cos^{-1}(x)$ is simply $$f'(x)=\frac{1}{\sqrt{1+x^{2}}}-\frac{1}{\sqrt{1+x^{2}}}=0$$ If the derivative of a function is zero for all values, the function must be constant. For proof, integrating zero yields a constant.
