$(\sin^{-1} x)+ (\cos^{-1} x)^3$ How do I find the least and maximum value of  $(\sin^{-1}  x)+ (\cos^{-1}  x)^3$ ? 
I have tried the formula $(a+b)^3=a^3 + b^3 +3ab(a+b)$ , but seem to reach nowhere near ?

If $a+b=k,$
Method $\#1:$
$$a^3+b^3=(a+b)^3-3ab(a+b)=k^3-3kab$$
Now $$(a+b)^2-4ab=(a-b)^2\ge0\iff-4ab\ge-(a+b)^2$$
Method $\#2:$
$$a^3+b^3=a^3+(k-a)^3=k^3-3k^2a+3ka^2=k^3+3k\left(a^2-ka\right)$$
Now $a^2-ka=\dfrac{(2a-k)^2-k^2}4\ge-\dfrac{k^2}4$
For both methods, here $$k=\dfrac\pi2$$
