Question

How do you prove `cos^-1(-x)+cos^-1x=pi`?

Answer 1

Please see below.

Explanation:

Let `cosA=x` then `cos(pi-A)=-cosA=-x`

Hence `cos^(-1)x=A`

and `cos^(-1)(-x)=pi-A`

adding the two

`cos^(-1)(-x)+cos^(-1)x=pi-A+A=pi`