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

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

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

prove

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

True

Solution steps

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

Manipulating left side

cos (x) cot (x)

Express with sin, cos

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

Rewrite using trig identities

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

\frac{sin ( x )}{cos ( x )} = tan (x)

tan (\frac{π}{2} - x) sec (x) = csc (x)

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