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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

Cancel the common factor:

sin (x)

= cos (x) cos (x)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

cos (x) cos (x) = cos^{1 + 1} (x)

= cos^{1 + 1} (x)

Add the numbers:

1 + 1 = 2

= cos^{2} (x)

= cos^{2} (x)

= cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

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