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

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

\frac{1}{( sec ( θ ) ) ^{2}} + \frac{1}{( csc ( θ ) ) ^{2}} = 1

sin^{2} (\frac{a}{2}) = \frac{1 - cos ( a )}{2}

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

cot (x) + tan (x) = sec (csc (x))

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