Is 1/(cot(x)(1-cos(2x)))=csc(2x) ?

The answer to whether 1/(cot(x)(1-cos(2x)))=csc(2x) is True

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prove 1/(cot(x)(1-cos(2x)))=csc(2x)

prove

\frac{1}{cot ( x ) ( 1 - cos ( 2 x ) )} = csc (2 x)

True

Solution steps

\frac{1}{cot ( x ) ( 1 - cos ( 2 x ) )} = csc (2 x)

Manipulating left side

\frac{1}{cot ( x ) ( 1 - cos ( 2 x ) )}

Rewrite using trig identities

= \frac{1}{2 sin ^{2} ( x ) cot ( x )}

Express with sin, cos

= \frac{1}{2 cos ( x ) sin ( x )}

Rewrite using trig identities

= \frac{1}{sin ( 2 x )}

Rewrite using trig identities

csc (2 x)

We showed that the two sides could take the same form

\Rightarrow True

tan^{4} (x) = tan^{2} (x) sec^{2} (x) - tan^{2} (x)

(tan (θ) + cot (θ)) cos (θ) = csc (θ)

cos^{4} (t) - sin^{4} (t) = 1 - 2 sin^{2} (t)

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

1 + tan^{2} (- θ) = sec^{2} (θ)

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