Is 1/(sin(x)cot(x))= 1/(cos(x)) ?

The answer to whether 1/(sin(x)cot(x))= 1/(cos(x)) is True

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prove 1/(sin(x)cot(x))= 1/(cos(x))

prove

\frac{1}{sin ( x ) cot ( x )} = \frac{1}{cos ( x )}

True

Solution steps

\frac{1}{sin ( x ) cot ( x )} = \frac{1}{cos ( x )}

Manipulating left side

\frac{1}{sin ( x ) cot ( x )}

Express with sin, cos

\frac{1}{cot ( x ) sin ( x )}

Use the basic trigonometric identity:

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

= \frac{1}{\frac{c o s ( x )}{s i n ( x )} sin ( x )}

Simplify

\frac{1}{\frac{c o s ( x )}{s i n ( x )} sin ( x )} : \frac{1}{cos ( x )}

\frac{1}{\frac{c o s ( x )}{s i n ( x )} sin ( x )}

Multiply

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

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

Multiply fractions:

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

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

Cancel the common factor:

sin (x)

= cos (x)

= \frac{1}{cos ( x )}

= \frac{1}{cos ( x )}

= \frac{1}{cos ( x )}

We showed that the two sides could take the same form

\Rightarrow True

Is 1/(sin(x)cot(x))= 1/(cos(x)) ?
The answer to whether 1/(sin(x)cot(x))= 1/(cos(x)) is True