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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

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

tan (x) (cot (x) + tan (x)) = sec^{2} (x)

\frac{1 + sin ( 2 x )}{sin ( 2 x )} = 1 + \frac{1}{2} sec (x) csc (x)

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

\frac{1}{csc ( x ) + 1} + \frac{1}{sin ( x ) + 1} = 1

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