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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

= \frac{csc ^{2} ( x )}{sec ^{2} ( x )}

Express with sin, cos

= \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

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

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

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)

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