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

1 Answer
Shwetank Mauria
Aug 2, 2016

Please see below.

Explanation:

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#

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