What is sin(arctan(4x)) ?

The solution to sin(arctan(4x)) is (4xsqrt(1+16x^2))/(1+16x^2)

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simplify sin(arctan(4x))

simplify

sin (arctan (4 x))

\frac{4 x 1 + 16 x ^{2}}{1 + 16 x ^{2}}

Solution steps

sin (arctan (4 x))

Use the following identity:

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

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

Simplify

= \frac{4 x 1 + 16 x ^{2}}{1 + 16 x ^{2}}

cos (arcsin (\frac{x}{8}))

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sin (3 \frac{π}{2} - α)

- cot (\frac{x}{2} + \frac{π}{4})

What is sin(arctan(4x)) ?
The solution to sin(arctan(4x)) is (4xsqrt(1+16x^2))/(1+16x^2)