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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

= - \frac{1}{sin ( x )}

Rewrite using trig identities

- csc (x)

We showed that the two sides could take the same form

\Rightarrow True

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

cos (θ) - sin (θ) sin (2 θ) = cos (θ) cos (2 θ)

1 + (cot (A))^{2} = \cdot (csc (A))^{2}

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

\frac{1}{cos ^{2} ( x )} = 20

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