Is cot(y)=(sin(2y))/(1-cos(2y)) ?

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

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prove cot(y)=(sin(2y))/(1-cos(2y))

prove

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

True

Solution steps

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

Manipulating right side

\frac{sin ( 2 y )}{1 - cos ( 2 y )}

Rewrite using trig identities

= \frac{cos ( y )}{sin ( y )}

Use the basic trigonometric identity:

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

= cot (y)

We showed that the two sides could take the same form

\Rightarrow True

1 + \frac{1}{tan ^{2} ( α )} = \frac{1}{sin ^{2} ( α )}

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

sin (x) - tan (x) = \frac{1}{sec ( x ) tan ( x )}

\frac{sin ( t ) cos ( t )}{tan ( t )} = cos^{2} (t)

\frac{tan ( x )}{1 - cot ( x )} + \frac{cot ( x )}{1 - tan ( x )} = 1 + sec (x) sin (x)

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