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

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

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prove 1/(2cot(x)sin^2(x))=csc(2x)

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Manipulating right side

csc (2 x)

Express with sin, cos

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{tan ^{2} ( x )}{sec ( x ) - 1} = 1 + \frac{1}{cos ( x )}

cos (α + β) - cos (α - β) = - 2 sin (α) cos (β)

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

7 sec (θ) = \frac{7 sec ( θ ) - 7}{1 - cos ( θ )}

2 tan (x) sin (x) - 3 cos (x) = 2

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