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

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

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

prove

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

True

Solution steps

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

Manipulating left side

cot (x) - cot (x) cos^{2} (x)

Express with sin, cos

= \frac{cos ( x ) - cos ^{3} ( x )}{sin ( x )}

Factor

\frac{cos ( x ) - cos ^{3} ( x )}{sin ( x )} : \frac{cos ( x ) ( 1 - cos ^{2} ( x ) )}{sin ( x )}

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

Rewrite using trig identities

= sin (x) cos (x)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{1}{sec ( θ )} = arcsec (θ)

\frac{( cot ( x ) )}{( csc ( x ) )} = cos (x)

\frac{1 + cot ^{2} ( x )}{cot ^{2} ( x )} = sec^{2} (x)

sec^{2} (x) - tan^{2} (x) = sec (x) cos (x)

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