How do you verify the identify $costhetacscthetatantheta=1$ ?

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Answer 1 · 2016-08-02T15:11:16

Please see below.

All trigonometric ratios can be easily expressed in terms of $sintheta$ and $costheta$ .

For example, $tantheta=sintheta/costheta$ , $cottheta=costheta/sintheta$ , $sectheta=1/costheta$ and $csctheta=1/sintheta$

Hence, $costhetacscthetatantheta$

= $costhetaxx1/sinthetaxxsintheta/costheta$

= $color(red)(cancel(costheta))xx1/cancel(sintheta)xxcancel(sintheta)/color(red)(cancel(costheta))$

= $1$

How do you verify the identify costhetacscthetatantheta=1costhetacscthetatantheta=1?