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

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

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

prove

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

True

Solution steps

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

Manipulating right side

\frac{1}{cot ( x )}

Express with sin, cos

\frac{1}{cot ( x )}

Use the basic trigonometric identity:

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

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

Simplify

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

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

Apply the fraction rule:

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

2 tan (x) = \frac{sin ( 2 x )}{1 - sin ^{2} ( x )}

(1 - cos (x)) (1 + sec (x)) = 1

\frac{sec ^{2} ( x ) - 1}{1 + tan ^{2} ( x )} = sin^{2} (x)

cos^{2} (9 θ) - sin^{2} (9 θ) = cos (18 θ)

sec (x) csc (x) = 2 csc (2 x)

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