What is sin(arctan(e^x)) ?

The solution to sin(arctan(e^x)) is (e^xsqrt(1+e^{2x)})/(1+e^{2x)}

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simplify sin(arctan(e^x))

simplify

sin (arctan (e^{x}))

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

Solution steps

sin (arctan (e^{x}))

Use the following identity:

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

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

Simplify

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

sin (arcsin (θ))

cos (x + 6 0^{\circ}) - (x - 60)

sin (x + 0.5 π)

cos (θ - 2 π)

sec (arctan (\frac{y}{x}))

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