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

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

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

prove

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

True

Solution steps

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

Manipulating left side

sin (x) - csc (x)

Express with sin, cos

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

Rewrite using trig identities

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

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

We showed that the two sides could take the same form

\Rightarrow True

sec^{2} (x) - sec^{2} (x) cos^{2} (x) = tan^{2} (x)

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

\frac{2}{tan ( x ) + cot ( x )} = sin (2 x)

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

tan^{4} (k) - sec^{4} (k) = 1 - 2 sec^{2} (k)

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