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

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

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

prove

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

True

Solution steps

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

Expand

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

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

We showed that the two sides could take the same form

\Rightarrow True

tan (θ) = \frac{sec ( θ )}{csc ( θ )}

\frac{sec ( θ )}{csc ^{2} ( θ )} = sec (θ) - cos (θ)

cos (3 β) = cos (β) (cos^{2} (β) - 3 sin^{2} (β))

sec^{2} (θ) cot^{2} (θ) - 1 = cot^{2} (θ)

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

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