1. ## Inverse circular function

If $\arcsin(x-\frac{x^2}{4}+\frac{x^3}{6}-....)+\arccos(x^2-\frac{x^4}{2}+\frac{x^6}{4}....)=\frac{\pi}{2},for 0<|x|<\sqrt2$. Then x equals

2. ## Re: Inverse circular function

first convince yourself that

$\arcsin(u)+\arccos(v)=\dfrac \pi 2 \Rightarrow u=v$

then determine what function each of the series represents

hint: Look at the series of $\ln(1+x)$ and adjust it as necessary

Then solve for these two functions being equal to each other.

Alternatively you might be able to solve for the values where the two series directly are equal.