Is 1/(tan(x))=csc(x)cos(x) ?

The answer to whether 1/(tan(x))=csc(x)cos(x) is True

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prove 1/(tan(x))=csc(x)cos(x)

prove

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

True

Solution steps

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

Manipulating left side

\frac{1}{tan ( x )}

Express with sin, cos

\frac{1}{tan ( x )}

Use the basic trigonometric identity:

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

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

Simplify

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

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

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

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

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

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

Rewrite using trig identities

Use the basic trigonometric identity:

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

\frac{cos ( x )}{\frac{1}{c s c ( x )}}

Simplify

\frac{cos ( x )}{\frac{1}{c s c ( x )}}

Apply the fraction rule:

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

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

Apply rule

\frac{a}{1} = a

= cos (x) csc (x)

cos (x) csc (x)

cos (x) csc (x)

= csc (x) cos (x)

We showed that the two sides could take the same form

\Rightarrow True

csc^{2} (x) (1 - cos^{2} (x)) = sin (648 0^{\circ})

- 2 cos^{4} (x) = - 2 (cos^{2} (x)) (cos^{2} (x))

csc (θ) = \frac{tan ( θ ) cot ( θ )}{sin ( θ )}

sin (x) cos (x) - 2 tan (x) = tan (x) cos (2 x)

cot^{2} (x) - cos^{2} (x) = cot^{2} (x) cot (x)

Is 1/(tan(x))=csc(x)cos(x) ?
The answer to whether 1/(tan(x))=csc(x)cos(x) is True