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

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

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

prove

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

True

Solution steps

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

Manipulating right side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

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

Simplify

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

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

Cancel the common factor:

sin (x)

= cos (x)

= cos (x)

= cos (x)

We showed that the two sides could take the same form

\Rightarrow True

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