What is sin(arctan(2a)) ?

The solution to sin(arctan(2a)) is (2asqrt(1+4a^2))/(1+4a^2)

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simplify sin(arctan(2a))

simplify

sin (arctan (2 a))

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

Solution steps

sin (arctan (2 a))

Use the following identity:

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

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

Simplify

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

\frac{1}{tan ( \frac{7 π}{2} - x )}

\frac{1}{sec ^{2} ( x ) - 1}

- 3 sin (4 x + \frac{π}{2})

tan (arctan (\frac{1}{x}))

12 a \cdot sin (850 \cdot t - 0.23)

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