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

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

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prove (csc^2(x))/(sec^2(x))=csc^2(x)-1

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

csc^{2} (x) - 1

We showed that the two sides could take the same form

\Rightarrow True

2 csc (2 x) = csc^{2} (x) tan (x)

\frac{sec ^{2} ( t )}{tan ( t )} = cot (t) + tan (t)

csc (\frac{π}{2} - x) = sec (x)

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

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

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