Is (cot(4u)-1)/(cot(4u)+1)=(1-tan(4u))/(1+tan(4u)) ?

The answer to whether (cot(4u)-1)/(cot(4u)+1)=(1-tan(4u))/(1+tan(4u)) is True

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prove (cot(4u)-1)/(cot(4u)+1)=(1-tan(4u))/(1+tan(4u))

prove

\frac{cot ( 4 u ) - 1}{cot ( 4 u ) + 1} = \frac{1 - tan ( 4 u )}{1 + tan ( 4 u )}

True

Solution steps

\frac{cot ( 4 u ) - 1}{cot ( 4 u ) + 1} = \frac{1 - tan ( 4 u )}{1 + tan ( 4 u )}

Manipulating left side

\frac{cot ( 4 u ) - 1}{cot ( 4 u ) + 1}

Express with sin, cos

= \frac{cos ( 4 u ) - sin ( 4 u )}{cos ( 4 u ) + sin ( 4 u )}

Manipulating right side

\frac{1 - tan ( 4 u )}{1 + tan ( 4 u )}

Express with sin, cos

= \frac{cos ( 4 u ) - sin ( 4 u )}{cos ( 4 u ) + sin ( 4 u )}

We showed that the two sides could take the same form

\Rightarrow True

sin (- x) = sin (x - π)

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

sin (4 a) = 4 sin (a) cos (a) cos (2 a)

3 cos^{2} (x) - 2 = 1 - 3 sin^{2} (x)

tan (\frac{a}{2}) = \frac{sin ( a )}{1 + cos ( a )}

Is (cot(4u)-1)/(cot(4u)+1)=(1-tan(4u))/(1+tan(4u)) ?
The answer to whether (cot(4u)-1)/(cot(4u)+1)=(1-tan(4u))/(1+tan(4u)) is True