Is (1+tan(x))/(1-tan(x))+(1+cot(x))/(1-cot(x))=0 ?

The answer to whether (1+tan(x))/(1-tan(x))+(1+cot(x))/(1-cot(x))=0 is True

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prove (1+tan(x))/(1-tan(x))+(1+cot(x))/(1-cot(x))=0

prove

\frac{1 + tan ( x )}{1 - tan ( x )} + \frac{1 + cot ( x )}{1 - cot ( x )} = 0

True

Solution steps

\frac{1 + tan ( x )}{1 - tan ( x )} + \frac{1 + cot ( x )}{1 - cot ( x )} = 0

Manipulating left side

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

Express with sin, cos

= 0

We showed that the two sides could take the same form

\Rightarrow True

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

tan (x) (1 - sin^{2} (x)) = \frac{1}{2} sin (2 x)

sin^{2} (x) + cos^{2} (x) = sin (x) csc (x)

(1 - sin^{2} (θ)) (1 + tan^{2} (θ)) = 1

sin (x) + cos (x) \cdot cot (x) = csc (x)

Is (1+tan(x))/(1-tan(x))+(1+cot(x))/(1-cot(x))=0 ?
The answer to whether (1+tan(x))/(1-tan(x))+(1+cot(x))/(1-cot(x))=0 is True