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

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

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

simplify

tan (\frac{π}{4} - arctan (x))

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

Solution steps

tan (\frac{π}{4} - arctan (x))

Rewrite using trig identities

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

Use the following identity:

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

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

Simplify

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

csc (\frac{π}{2} - θ)

cos (\frac{π}{2} + π \frac{n}{2})

cos (3 t - \frac{π}{2})

cos (3 x + \frac{π}{4})

27.85 sin (12.78 t + 0.569)

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