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

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

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

prove

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

True

Solution steps

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

Manipulating left side

\frac{cos ^{2} ( x )}{cot ( x )}

Express with sin, cos

\frac{cos ^{2} ( x )}{cot ( x )}

Use the basic trigonometric identity:

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

= \frac{cos ^{2} ( x )}{\frac{c o s ( x )}{s i n ( x )}}

Simplify

\frac{cos ^{2} ( x )}{\frac{c o s ( x )}{s i n ( x )}} : cos (x) sin (x)

\frac{cos ^{2} ( x )}{\frac{c o s ( x )}{s i n ( x )}}

Apply the fraction rule:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

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

Cancel the common factor:

cos (x)

= cos (x) sin (x)

= cos (x) sin (x)

= cos (x) sin (x)

= sin (x) cos (x)

We showed that the two sides could take the same form

\Rightarrow True

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2 sin (x) cos (x) + 4 cos (2 x) = 1

3 - 6 sin^{2} (x) = 3 cos (2 x)

1 + cos (2 x) = 3 sin (x)

sin^{2} (2 θ) = \frac{1 - cos ( 4 θ )}{2}

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