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

The solution to arctan(sin(arctan(x))) is arctan((xsqrt(1+x^2))/(1+x^2))

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simplify arctan(sin(arctan(x)))

simplify

arctan (sin (arctan (x)))

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

Solution steps

arctan (sin (arctan (x)))

Use the following identity:

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

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

Remove parentheses:

(a) = a

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

\frac{1}{2} tan (x + \frac{π}{4})

3 cos (2 θ - 6 0^{\circ}) - 2

sin (\frac{x}{2} + \frac{π}{2})

sin^{2} (x - \frac{π}{4})

cos (π - t)

What is arctan(sin(arctan(x))) ?
The solution to arctan(sin(arctan(x))) is arctan((xsqrt(1+x^2))/(1+x^2))