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

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

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simplify sin(arctan(x/5))

simplify

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

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

Solution steps

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

Use the following identity:

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

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

Simplify

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

cos (arcsin (\frac{4}{x}))

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cos (18 0^{\circ} + x)

tan (\frac{π}{4} - x)

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