What is sin(arctan(1/x)) ?

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

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simplify sin(arctan(1/x))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

cot (π - θ)

sin (27 0^{\circ} + x)

cos (π + x) + cos (x - π)

cos (2 x + \frac{π}{2})

sin (27 0^{\circ} - x)

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