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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

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

Manipulating right side

cot (x) csc (x)

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

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

sin^{2} (θ) - cos^{2} (θ) = 1

tan^{2} (θ) csc^{2} (θ) = sec^{2} (θ)

(tan (x) + cot (x))^{2} = sec^{4} (x) cot^{2} (x)

(1 + tan^{2} (s)) (1 - sin^{2} (s)) = 1

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