What is sin(-arctan(x)) ?

The solution to sin(-arctan(x)) is -(xsqrt(1+x^2))/(1+x^2)

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simplify sin(-arctan(x))

simplify

sin (- arctan (x))

- \frac{x 1 + x ^{2}}{1 + x ^{2}}

Solution steps

sin (- arctan (x))

Use the negative angle identity:

sin (- x) = - sin (x)

= - sin (arctan (x))

Use the following identity:

sin (arctan (x)) = \frac{x 1 + x ^{2}}{1 + x ^{2}}

= - (\frac{x 1 + x ^{2}}{1 + x ^{2}})

Remove parentheses:

(a) = a

= - \frac{x 1 + x ^{2}}{1 + x ^{2}}

tan (a - 9 0^{\circ}) sin (- a)

cos (arccos (8 x))

sin (g + π)

sin^{2} (9 0^{\circ} - x)

sin (4 5^{\circ} - x)

What is sin(-arctan(x)) ?
The solution to sin(-arctan(x)) is -(xsqrt(1+x^2))/(1+x^2)