Is cot(θ)=(sin(2θ))/(1-cos(2θ)) ?

The answer to whether cot(θ)=(sin(2θ))/(1-cos(2θ)) is True

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prove cot(θ)=(sin(2θ))/(1-cos(2θ))

prove

cot (θ) = \frac{sin ( 2 θ )}{1 - cos ( 2 θ )}

True

Solution steps

cot (θ) = \frac{sin ( 2 θ )}{1 - cos ( 2 θ )}

Manipulating right side

\frac{sin ( 2 θ )}{1 - cos ( 2 θ )}

Rewrite using trig identities

= \frac{cos ( θ )}{sin ( θ )}

Use the basic trigonometric identity:

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

= cot (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

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

cot (x) = \frac{1}{tan ( x )}

Is cot(θ)=(sin(2θ))/(1-cos(2θ)) ?
The answer to whether cot(θ)=(sin(2θ))/(1-cos(2θ)) is True