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

1 Answer

Apr 7, 2018

$x = 0$

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:

enter image source here

Hopefully this helps!

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