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

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

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simplify sin(arctan(x/d))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

tan (arcsin (t))

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

f (x) 5 sin (x + π)

cot^{2} (- csc^{2} (x))

- 2 cos (x + π) - 7

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