What is sin(arctan(5/x)) ?

The solution to sin(arctan(5/x)) is (5sqrt(x^2+25))/(x^2+25)

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simplify sin(arctan(5/x))

simplify

sin (arctan (\frac{5}{x}))

\frac{5 x ^{2} + 25}{x ^{2} + 25}

Solution steps

sin (arctan (\frac{5}{x}))

Use the following identity:

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

= \frac{( \frac{5}{x} ) 1 + ( \frac{5}{x} ) ^{2}}{1 + ( \frac{5}{x} ) ^{2}}

Simplify

= \frac{5 x ^{2} + 25}{x ^{2} + 25}

sin (2) (π + x) - cos (π + x)

tan^{2} (θ) + 1

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

cot (π - x)

sin (x + \frac{π}{3}) + 1

What is sin(arctan(5/x)) ?
The solution to sin(arctan(5/x)) is (5sqrt(x^2+25))/(x^2+25)