Is (cos(θ))/(sin(θ)cot(θ))=1 ?

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

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prove (cos(θ))/(sin(θ)cot(θ))=1

prove

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

True

Solution steps

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

Manipulating left side

\frac{cos ( θ )}{sin ( θ ) cot ( θ )}

Express with sin, cos

\frac{cos ( θ )}{cot ( θ ) sin ( θ )}

Use the basic trigonometric identity:

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

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

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

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

Multiply

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

\frac{cos ( θ )}{sin ( θ )} sin (θ)

Multiply fractions:

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

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

Cancel the common factor:

sin (θ)

= cos (θ)

= \frac{cos ( θ )}{cos ( θ )}

Apply rule

\frac{a}{a} = 1

= 1

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

2 cot (θ) cot (2 θ) = cot^{2} (θ) - 1

csc (u) - cot (u) = \frac{sin ( u )}{1 + cos ( u )}

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

cos^{2} (x) = \frac{1}{2} (1 + cos (2 x))

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

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