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

The solution to sin(arctan(a/b)) is (asqrt(b^2+a^2))/(b^2+a^2)

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simplify sin(arctan(a/b))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

sin (x - 18 0^{\circ})

tan (18 0^{\circ} + x) cot (- x)

sin (t + π)

tan (arcsin (u))

cos (t - \frac{π}{6})

What is sin(arctan(a/b)) ?
The solution to sin(arctan(a/b)) is (asqrt(b^2+a^2))/(b^2+a^2)