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

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

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

prove

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

True

Solution steps

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

Manipulating right side

sec^{2} (x) - 1

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

cot (b) sin (b) = cos (b)

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

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

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