Is ((cot(a)))/((csc(a)))=cos(a) ?

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

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prove ((cot(a)))/((csc(a)))=cos(a)

prove

\frac{( cot ( a ) )}{( csc ( a ) )} = cos (a)

True

Solution steps

\frac{cot ( a )}{csc ( a )} = cos (a)

Manipulating left side

\frac{cot ( a )}{csc ( a )}

Express with sin, cos

\frac{cot ( a )}{csc ( a )}

Use the basic trigonometric identity:

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

= \frac{\frac{c o s ( a )}{s i n ( a )}}{csc ( a )}

Use the basic trigonometric identity:

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

= \frac{\frac{c o s ( a )}{s i n ( a )}}{\frac{1}{s i n ( a )}}

Simplify

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

\frac{\frac{c o s ( a )}{s i n ( a )}}{\frac{1}{s i n ( a )}}

Divide fractions:

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

= \frac{cos ( a ) sin ( a )}{sin ( a ) \cdot 1}

Refine

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

Cancel the common factor:

sin (a)

= cos (a)

= cos (a)

= cos (a)

We showed that the two sides could take the same form

\Rightarrow True

cos (\frac{π}{12}) = \frac{2 + 3}{2}

tan (θ) = tan (θ) + 2

tan (2 u) = \frac{2 tan ( u )}{1 - tan ^{2} ( u )}

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

cot (\frac{π}{2} - θ) = tan (θ)

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