Is (1-tan(θ))/(1+tan(θ))=(cot(θ)-1)/(cot(θ)+1) ?

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

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prove (1-tan(θ))/(1+tan(θ))=(cot(θ)-1)/(cot(θ)+1)

prove

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

True

Solution steps

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

Manipulating left side

\frac{1 - tan ( θ )}{1 + tan ( θ )}

Express with sin, cos

= \frac{cos ( θ ) - sin ( θ )}{cos ( θ ) + sin ( θ )}

Manipulating right side

\frac{cot ( θ ) - 1}{cot ( θ ) + 1}

Express with sin, cos

= \frac{cos ( θ ) - sin ( θ )}{cos ( θ ) + sin ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

sec (x) + csc (x) = csc (x) (tan (x) + 1)

cos (θ + \frac{3 π}{2}) = sin (θ)

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