What is simplify-tan(arctan(x)+pi/4) ?

The solution to simplify-tan(arctan(x)+pi/4) is -(x+1)/(1-x)

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simplify-tan(arctan(x)+pi/4)

simplify

- tan (arctan (x) + \frac{π}{4})

- \frac{x + 1}{1 - x}

Solution steps

- tan (arctan (x) + \frac{π}{4})

Rewrite using trig identities

= - \frac{sin ( arctan ( x ) ) + cos ( arctan ( x ) )}{cos ( arctan ( x ) ) - sin ( arctan ( x ) )}

Use the following identity:

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

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

Use the following identity:

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

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

Simplify

= - \frac{x + 1}{1 - x}

csc (30 π + x)

e^{3 x} sin^{2} (- 3 y)

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

- 2 sin (4 x) \cdot sin (- x)

sin (- 2 x) cos (- 2 x)

What is simplify-tan(arctan(x)+pi/4) ?
The solution to simplify-tan(arctan(x)+pi/4) is -(x+1)/(1-x)