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

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

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

prove

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

True

Solution steps

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

Manipulating left side

tan (\frac{π}{4} - t)

Rewrite using trig identities

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

Manipulating right side

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

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

- tan (x) = tan (- x)

\frac{csc ( θ ) + sin ( θ )}{tan ( θ ) + 1} = csc (θ)

- sin^{2} (x) - cos^{2} (x) = - 1

sin (3 θ) = 3 cos^{2} (θ) sin (θ) - sin^{3} (θ)

\frac{tan ( θ ) cos ( θ )}{sin ( θ )} = 1

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