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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

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

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

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

Multiply

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

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

Multiply fractions:

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

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

Cancel the common factor:

sin (x)

= cos (x)

= \frac{cos ( x )}{cos ( 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} (θ) cos (θ) sec (θ) = 1 - cos^{2} (θ)

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

tan^{2} (θ) - tan^{2} (θ) sin^{2} (θ) = sin^{2} (θ)

tan (x) + cot (x) = cot (x) sec^{2} (x)

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

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