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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

= tan (x)

We showed that the two sides could take the same form

\Rightarrow True

tan (θ) cot (θ) - sin^{2} (θ) = cos^{2} (θ)

sin (2 x) = \frac{2 cot ( x )}{1 + cot ^{2} ( x )}

sec (θ) = \frac{1}{cos ( θ )}

csc (2 θ) = \frac{csc ( θ )}{2 cos ( θ )}

sin (- x) + csc (x) = cot (x) cos (x)

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