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

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

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

prove

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

True

Solution steps

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

Manipulating left side

cos (x) csc (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

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

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

\frac{cot ( θ )}{csc ( θ )} = cos (θ)

tan (t) + \frac{cos ( t )}{1 + sin ( t )} = sec (t)

cos^{2} (x) = 1 - sin^{2} (x)