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

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

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

prove

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

True

Solution steps

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

Manipulating left 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

\frac{csc ^{2} ( x )}{2 cot ( x )} = csc (2 x)

cot (θ) sin (θ) = cos (θ)

cot (x) (sec^{2} (x) - 1) = tan (x)

(1 - cos (x)) (1 + cos (x)) = sin^{2} (x)

(1 + sin (θ)) (1 - sin (θ)) = cos^{2} (θ)

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