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

The solution to sin(arctan(x/a)) is (xsqrt(a^2+x^2))/(a^2+x^2)

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simplify sin(arctan(x/a))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

- sin (- 2 x)

tan (π - x) cos (- x) + sin (π + x)

cos (- π + nπ)

tan (θ - π)

cos (x + 7 π)

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