What is csc(arctan((1-x)/(1+x))) ?

The solution to csc(arctan((1-x)/(1+x))) is (sqrt(2x^2+2))/(1-x)

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simplify csc(arctan((1-x)/(1+x)))

simplify

csc (arctan (\frac{1 - x}{1 + x}))

\frac{2 x ^{2} + 2}{1 - x}

Solution steps

csc (arctan (\frac{1 - x}{1 + x}))

Use the following identity:

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

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

Simplify

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

cos (2 (t + \frac{π}{2}))

tan (π - θ) + tan (π + θ)

- a cos (\frac{π}{2} - b x)

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

cos (5 π - x)

What is csc(arctan((1-x)/(1+x))) ?
The solution to csc(arctan((1-x)/(1+x))) is (sqrt(2x^2+2))/(1-x)