What is sin(arctan(2x)) ?

The solution to sin(arctan(2x)) is (2xsqrt(1+4x^2))/(1+4x^2)

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simplify sin(arctan(2x))

simplify

sin (arctan (2 x))

\frac{2 x 1 + 4 x ^{2}}{1 + 4 x ^{2}}

Solution steps

sin (arctan (2 x))

Use the following identity:

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

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

Simplify

= \frac{2 x 1 + 4 x ^{2}}{1 + 4 x ^{2}}

\frac{cos ( nπ )}{n ^{2}}

\frac{d x}{sec ^{2} ( x )}

cos (sin (- 1 (x)))

sin (t + 2 π)

tan (π - a)

What is sin(arctan(2x)) ?
The solution to sin(arctan(2x)) is (2xsqrt(1+4x^2))/(1+4x^2)