Is csc(x)cos(x)=cot(x) ?

The answer to whether csc(x)cos(x)=cot(x) is True

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prove csc(x)cos(x)=cot(x)

prove

csc (x) cos (x) = cot (x)

True

Solution steps

csc (x) cos (x) = cot (x)

Manipulating left side

csc (x) cos (x)

Express with sin, cos

csc (x) cos (x)

Use the basic trigonometric identity:

csc (x) = \frac{1}{sin ( x )}

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

Simplify

\frac{1}{sin ( x )} cos (x) : \frac{cos ( x )}{sin ( x )}

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

Multiply fractions:

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

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

Multiply:

1 \cdot cos (x) = cos (x)

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

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

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

Use the basic trigonometric identity:

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

= cot (x)

We showed that the two sides could take the same form

\Rightarrow True

p ro v e sin (π - x) = sin (x)

p ro v e cos (θ) csc (θ) = cot (θ)

p ro v e cot (- x) sin (x) = - cos (x)

p ro v e sin (3 π - x) = sin (x)

p ro v e sin^{2} (θ) = \frac{1 - cos ( 2 θ )}{2}