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

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

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

cos (x) + sin (x) (tan (x)) = sec (x)

cot^{2} (x) + \frac{1}{cos ( x ) sec ( x )} = csc^{2} (x)

\frac{1 + cos ( θ )}{sin ( θ )} = csc (θ) + cot (θ)

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