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

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

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

prove

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

True

Solution steps

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

Manipulating left side

tan (θ + \frac{π}{4})

Rewrite using trig identities

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

Manipulating right side

\frac{1 + tan ( θ )}{1 - tan ( θ )}

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

tan (θ) = \frac{1}{cot ( θ )}

cos (x) tan (x) sec (- x) = sin (x) - 1

sin (x) = cos (x - \frac{π}{2})

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

tan^{4} (x) - sec^{4} (x) = - 2 tan^{2} (x) - 1

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