What is sin(arctan(x-2)) ?

The solution to sin(arctan(x-2)) is ((x-2)sqrt(x^2-4x+5))/(x^2-4x+5)

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simplify sin(arctan(x-2))

simplify

sin (arctan (x - 2))

\frac{( x - 2 ) x ^{2} - 4 x + 5}{x ^{2} - 4 x + 5}

Solution steps

sin (arctan (x - 2))

Use the following identity:

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

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

Simplify

= \frac{( x - 2 ) x ^{2} - 4 x + 5}{x ^{2} - 4 x + 5}

π sec (3 x + \frac{π}{2}) - 1

tan (arctan (\frac{x}{2}))

sin (\frac{1}{4} π + x)

sin (a) - sin (- a)

(tan (x))^{2} + 1

What is sin(arctan(x-2)) ?
The solution to sin(arctan(x-2)) is ((x-2)sqrt(x^2-4x+5))/(x^2-4x+5)