Question

An interesting question in inverse trigonometry :D !

Answer 1

While defining inverse trigonometric function,a new system is followed where principal values have been redefined as follows:
Function->Domain->Principle Value
\[\LARGE \sin^{-1}x---->[-1,1]--->[\frac{\pi}{2},\frac{3\pi}{2}]\]
\[\LARGE \cos^{-1}x---->[-1,1]--->[{\pi},2 \pi]\]
Based on the above system,answer the following.
1)The value of arcsinx+arccosx=?
2)The value of arcsinx=?

Answer 2

2) The value of arcsin(-x)=?*