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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

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

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

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

tan (\frac{π}{3}) sin (\frac{2 π}{3}) = 1 + sin (\frac{π}{6})

2 cot (x) + cos (x) - sec (x) = cot (x)

(tan (θ) + cot (θ)) sin (θ) cos (θ) = 1

3 (tan (x)) + 12 = 3

2 cos (x) tan (x) cot (x) = 2

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