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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

= \frac{cos ^{2} ( x ) + sin ^{2} ( x )}{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

(1 - cos (θ)) (1 + cos (θ)) (1 + cot^{2} (θ)) = 1

tan^{2} (θ) - sin^{2} (θ) = sin^{2} (θ) tan^{2} (θ)

cos^{2} (2 u) - sin^{2} (2 u) = cos (4 u)

tan (u) cot (u) - cos^{2} (u) = sin^{2} (u)

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

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