Is tan(pi/4-x)=(1-tan(x))/(1+tan(x)) ?

The answer to whether tan(pi/4-x)=(1-tan(x))/(1+tan(x)) is True

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prove tan(pi/4-x)=(1-tan(x))/(1+tan(x))

prove

tan (\frac{π}{4} - x) = \frac{1 - tan ( x )}{1 + tan ( x )}

True

Solution steps

tan (\frac{π}{4} - x) = \frac{1 - tan ( x )}{1 + tan ( x )}

Manipulating left side

tan (\frac{π}{4} - x)

Rewrite using trig identities

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

Manipulating right side

\frac{1 - tan ( x )}{1 + tan ( x )}

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

(sin (x) + cos (x)) 2 = 1 + 2 sin (x) cos (x)

cos (3 x) = \frac{2}{2}

cos (x) (sec (x) tan (x)) = tan (x)

cos (x) = \frac{sin ( x )}{tan ( x )}

cot^{2} (x) \cdot sec^{2} (x) = csc^{2} (x)

Is tan(pi/4-x)=(1-tan(x))/(1+tan(x)) ?
The answer to whether tan(pi/4-x)=(1-tan(x))/(1+tan(x)) is True