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

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

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

prove

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

True

Solution steps

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

Manipulating left side

csc^{2} (x) cos^{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

1 - 2 cos^{2} (x) + cos^{4} (x) = sin^{4} (x)

sec (x) - \frac{cos ( x )}{1 + sin ( x )} = tan (x)

tan (x) + cot (x) = (sec (x)) (csc (x))

sin (x) + sin (x) tan^{2} (x) = tan (x) sec (x)

sin (θ) (csc (θ) - sin (θ)) = cos^{2} (θ)

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