What is sin(arctan(y)) ?

The solution to sin(arctan(y)) is (ysqrt(1+y^2))/(1+y^2)

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simplify sin(arctan(y))

simplify

sin (arctan (y))

\frac{y 1 + y ^{2}}{1 + y ^{2}}

Solution steps

sin (arctan (y))

Use the following identity:

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

= \frac{y 1 + y ^{2}}{1 + y ^{2}}

tan (arctan (2 x))

cos (3 t - 6 π)

3 cot (θ - \frac{π}{6}) + 1

sin (2 x - \frac{π}{4})

cot (arccos (\frac{x}{13}))

What is sin(arctan(y)) ?
The solution to sin(arctan(y)) is (ysqrt(1+y^2))/(1+y^2)