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

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

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

prove

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

True

Solution steps

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

Manipulating left side

\frac{sin ^{2} ( t )}{tan ( t )}

Express with sin, cos

\frac{sin ^{2} ( t )}{tan ( t )}

Use the basic trigonometric identity:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Cancel the common factor:

sin (t)

= sin (t) cos (t)

= sin (t) cos (t)

= cos (t) sin (t)

= sin (t) cos (t)

We showed that the two sides could take the same form

\Rightarrow True

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