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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

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

Simplify

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

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

Cancel the common factor:

cos (x)

= sin (x)

= sin (x)

= sin (x)

We showed that the two sides could take the same form

\Rightarrow True

tan^{2} (x) (csc^{2} (x) - 1) = 1

cos (x) csc (x) = cot (x)

csc (x) = \frac{1}{sin ( x )}

\frac{cos ( θ )}{1 - sin ( θ )} = sec (θ) + tan (θ)

\frac{cot ( θ )}{csc ( θ )} = cos (θ)

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