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

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

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

prove

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

True

Solution steps

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

Manipulating left side

tan (x + \frac{π}{4})

Rewrite using trig identities

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

Manipulating right side

\frac{tan ( x ) + 1}{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

csc (θ) cos (θ) tan (θ) = 1

sin (θ) cos (φ) = \frac{sin ( θ + φ ) + sin ( θ - φ )}{2}

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

\frac{cos ( x )}{sin ( x )} = cos^{2} (x)

sin (α + β) + sin (α - β) = 2 sin (α) cos (β)

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