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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Manipulating right side

tan (x + \frac{π}{4})

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

4 sin (x) cos (x) = 2 sin (2 x)

sin^{2} (a) cos^{2} (a) + cos^{4} (a) = cos^{2} (a)

\frac{cot ( θ )}{cos ( θ )} = csc (θ)

cos^{2} (2 x) = \frac{1}{2} (1 + cos (4 x))

sin (4 x) = 8 sin (x) cos (3 x) - 4 sin (x) cos (x)

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