$$\int\frac{1}{\sqrt{a^2-x^2}}dx=\sin^{-1}(\frac{x}{a})+C=-\cos^{-1}(\frac{x}{a})+C , \text{for} \space |x|<a$$ Can someone why they are equal explain ?
2026-04-04 18:52:54.1775328774
What is the relation between $sin^{-1}x$ and $cos^{-1}x$
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They are not different, since $\arcsin(x)+\arccos(x)=\frac\pi2$, for each $x\in[-1,1]$. So$$\arcsin\left(\frac xa\right)+C=-\arccos\left(\frac xa\right)+\frac\pi2+C.$$