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

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

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prove csc^2(x)(1-sin^2(x))=cot^2(x)

prove

csc^{2} (x) (1 - sin^{2} (x)) = cot^{2} (x)

True

Solution steps

csc^{2} (x) (1 - sin^{2} (x)) = cot^{2} (x)

Manipulating right side

cot^{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 )}

Use the basic trigonometric identity:

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

sin (2 a) = 2 sin (a) cos (a)

tan (x + \frac{π}{2}) = - cot (x)

cos (θ) tan (θ) csc (θ) = 1

csc (x) + cot (x) = \frac{1}{csc ( x ) - cot ( x )}

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

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