Question

How do you solve Arcsin(x)+arctan(x) = 0?

Answer 1

`x = 0`

Explanation:

We have:

`arcsinx = -arctanx`

`sinx = -tanx`

`sinx + sinx/cosx = 0`

`(sinxcosx+ sinx)/cosx = 0`

`sinxcosx + sinx = 0`

`sinx(cosx + 1) = 0`

`sinx = 0 or cosx = -1`

`x = 0, pi`

Since the domain of `arcsinx` is `-1 ≤ x ≤ 1`, the only admissible solution is `x= 0`. The graph confirms:

Hopefully this helps!