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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

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

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

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

Multiply

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

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

Multiply fractions:

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

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

Cancel the common factor:

cos (x)

= sin (x)

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

Apply rule

\frac{a}{a} = 1

= 1

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

sin^{2} (x) = sin (x) csc (x) - cos^{2} (x)

sin (x) + cos (x) = 2

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

sin (x + x) = 2 sin (x) cos (x)

\frac{1 - sin ^{2} ( β )}{cos ( β )} = cos (β)

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