What is sin(arctan(u)) ?

The solution to sin(arctan(u)) is (usqrt(1+u^2))/(1+u^2)

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simplify sin(arctan(u))

simplify

sin (arctan (u))

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

Solution steps

sin (arctan (u))

Use the following identity:

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

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

tan (2 π + θ)

- 3 cos (x - \frac{π}{2})

- sin (θ - 9 0^{\circ})

cos^{2} (π - x)

sec (θ + 18 0^{\circ})

What is sin(arctan(u)) ?
The solution to sin(arctan(u)) is (usqrt(1+u^2))/(1+u^2)