What is sin(arctan((x-1)/(x+3))) ?

The solution to sin(arctan((x-1)/(x+3))) is ((x-1)sqrt(2x^2+4x+10))/(2x^2+4x+10)

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simplify sin(arctan((x-1)/(x+3)))

simplify

sin (arctan (\frac{x - 1}{x + 3}))

\frac{( x - 1 ) 2 x ^{2} + 4 x + 10}{2 x ^{2} + 4 x + 10}

Solution steps

sin (arctan (\frac{x - 1}{x + 3}))

Use the following identity:

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

= \frac{( \frac{x - 1}{x + 3} ) 1 + ( \frac{x - 1}{x + 3} ) ^{2}}{1 + ( \frac{x - 1}{x + 3} ) ^{2}}

Simplify

= \frac{( x - 1 ) 2 x ^{2} + 4 x + 10}{2 x ^{2} + 4 x + 10}

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What is sin(arctan((x-1)/(x+3))) ?
The solution to sin(arctan((x-1)/(x+3))) is ((x-1)sqrt(2x^2+4x+10))/(2x^2+4x+10)