Is (1+tan(θ))/(1+cot(θ))=tan(θ) ?

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

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prove (1+tan(θ))/(1+cot(θ))=tan(θ)

prove

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

True

Solution steps

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

Manipulating left side

\frac{1 + tan ( θ )}{1 + cot ( θ )}

Express with sin, cos

= \frac{sin ( θ )}{cos ( θ )}

Use the basic trigonometric identity:

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

= tan (θ)

We showed that the two sides could take the same form

\Rightarrow True

cos (x + 1) = cos (- x - 1)

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

\frac{tan ( θ )}{sin ( θ )} = sec (θ)

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

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

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