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

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

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prove (sin(x)-csc(x))/(csc(x))=-cos^2(x)

prove

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

True

Solution steps

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

Manipulating left side

\frac{sin ( x ) - csc ( x )}{csc ( x )}

Express with sin, cos

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

Rewrite using trig identities

= - cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

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

tan (2 x) - 2 tan (2 x) sin^{2} (x) = sin (2 x)

cot^{2} (θ) csc^{2} (θ) - cot^{2} (θ) = cot^{4} (θ)

sin (x - π) = - sin (x)

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

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