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

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

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Answer 1 · 2018-04-07T17:59:49

$x = 0$ $x = 0$

Explanation:

We have:

$arcsin x = - arctan x$ $arcsinx = -arctanx$

$sin x = - tan x$ $sinx = -tanx$

$sin x + \frac{sin x}{cos x} = 0$ $sinx + sinx/cosx = 0$

$\frac{sin x cos x + sin x}{cos x} = 0$ $(sinxcosx+ sinx)/cosx = 0$

$sin x cos x + sin x = 0$ $sinxcosx + sinx = 0$

$sin x (cos x + 1) = 0$ $sinx(cosx + 1) = 0$

$sin x = 0 or cos x = - 1$ $sinx = 0 or cosx = -1$

$x = 0, π$ $x = 0, pi$

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

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Hopefully this helps!

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

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