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

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

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prove (1+cos(2x))/(2sin^2(x))=cot^2(x)

prove

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

True

Solution steps

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

Manipulating left side

\frac{1 + cos ( 2 x )}{2 sin ^{2} ( x )}

Rewrite using trig identities

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

Rewrite using trig identities

cot^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

sec (θ - π) = - sec (θ)

cos (0 + \frac{π}{2}) = - sin (θ)

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

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

csc (x) tan (x) + sec (x) = 2 sec (x)

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