How do you verify the identity $1/(tanthetacsctheta)=costheta$ ?

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Answer 1 · 2017-01-17T19:11:42

see below

Left Hand Side:

$1/(tan theta csc theta) = 1/(sin theta / cos theta * 1/sin theta$

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

$=1/(1/costheta)$

$=1 * cos theta/ 1$

$= cos theta$

$:.=$ Right Hand Side

How do you verify the identity 1/(tanthetacsctheta)=costheta1/(tanthetacsctheta)=costheta?