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

The solution to sin(arctan(L/a)) is (Lsqrt(a^2+L^2))/(a^2+L^2)

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simplify sin(arctan(L/a))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

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What is sin(arctan(L/a)) ?
The solution to sin(arctan(L/a)) is (Lsqrt(a^2+L^2))/(a^2+L^2)