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) \cdot 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

cot (a) + tan (a) = 2 csc (2 a)

cot^{2} (x) = cos^{2} (x) + (cot (x) cos (x))^{2}

sin (- x) + cos (- x) = - sin (x) + cos (x)

cot (θ) sec (θ) sin (θ) = 1

\frac{sec ( θ )}{1 - sin ( θ )} = \frac{1 + sin ( θ )}{cos ^{3} ( θ )}