How do you simplify $cottheta/costheta$ ?

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Answer 1 · 2016-12-19T12:16:57

$cot theta/cos theta = csc theta$

$cot theta/cos theta = 1/tan theta * 1/cos theta$

$= cos theta/sin theta * 1/cos theta$

$= cancel cos theta/sin theta * 1/cancel cos theta = 1/sin theta$

$= csc theta$

Answer 2 · 2016-12-19T12:46:35

$csc(theta)$

We have: $(cot(theta)) / (cos(theta))$

First, let's apply the standard trigonometric identity $cot(theta) = (cos(theta)) / (sin(theta))$ :

$= ((cos(theta)) / (sin(theta))) / (cos(theta))$

$= (cos(theta)) / (sin(theta) cos(theta))$

$= (1) / (sin(theta))$

Then, let's apply the identity $csc(theta) = (1) / (sin(theta))$

$= csc(theta)$

How do you simplify cottheta/costhetacottheta/costheta?