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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

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

Use the basic trigonometric identity:

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

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

Simplify

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

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

Divide fractions:

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

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

Refine

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

Cancel the common factor:

sin (x)

= cos (x)

= cos (x)

= cos (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1 + cot ^{2} ( x )}{cot ^{2} ( x )} = sec^{2} (x)

sec^{2} (x) - tan^{2} (x) = sec (x) cos (x)

cos^{2} (4 x) = \frac{1}{2} + \frac{1}{2} cos (16 x)

- 3 sin (35) - 3 sin (15) = - 6 sin (25) cos (10)

\frac{( sec ^{2} ( t ) )}{sec ^{2} ( t ) - 1} = csc^{2} (t)

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