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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Cancel the common factor:

cos (t)

= cos (t) sin (t)

= cos (t) sin (t)

= cos (t) sin (t)

We showed that the two sides could take the same form

\Rightarrow True

\frac{( sin ( a ) + sin ( 3 a ) )}{cos ( a ) + cos ( 3 a )} = tan (2 a)

4 sec^{2} (θ) - 3 = 1 + 4 tan^{2} (θ)

sec (θ) = csc (θ) tan (θ)

- sin (x) = sin (x)

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

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