Is (cot(α))/(cos(α))=csc(α) ?

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

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prove (cot(α))/(cos(α))=csc(α)

prove

\frac{cot ( α )}{cos ( α )} = csc (α)

True

Solution steps

\frac{cot ( α )}{cos ( α )} = csc (α)

Manipulating left side

\frac{cot ( α )}{cos ( α )}

Express with sin, cos

\frac{cot ( α )}{cos ( α )}

Use the basic trigonometric identity:

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

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

Simplify

\frac{\frac{c o s ( α )}{s i n ( α )}}{cos ( α )} : \frac{1}{sin ( α )}

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

Apply the fraction rule:

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

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

Cancel the common factor:

cos (α)

= \frac{1}{sin ( α )}

= \frac{1}{sin ( α )}

= \frac{1}{sin ( α )}

Rewrite using trig identities

Use the basic trigonometric identity:

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

\frac{1}{\frac{1}{c s c ( α )}}

Simplify

\frac{1}{\frac{1}{c s c ( α )}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{csc ( α )}{1}

Apply rule

\frac{a}{1} = a

= csc (α)

csc (α)

csc (α)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{cos ( θ )}{sin ^{2} ( θ )} = 2 cos^{2} (θ)

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Is (cot(α))/(cos(α))=csc(α) ?
The answer to whether (cot(α))/(cos(α))=csc(α) is True