Is cos^2(x)csc^2(x)=csc^2(x)-1 ?

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

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prove cos^2(x)csc^2(x)=csc^2(x)-1

prove

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

True

Solution steps

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

Manipulating left side

cos^{2} (x) csc^{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

\frac{sec ( x ) + tan ( x )}{csc ( x ) + 1} = tan (x)

tan (a) = \frac{sec ( a )}{csc ( a )}

sec (x) tan (x) cos (x) cot (x) = 1

1 - sec (x) cos^{3} (x) = sin^{2} (x)

tan (3 π + θ) = tan (θ)

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