How do you verify the identity $cot^2t/csct=csct-sint$ ?

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Answer 1 · 2017-01-17T19:51:44

see below

Left Hand Side:

$cot^2 t / csc t = (cos^2 t / sin^2t)/(1/sint)$

$= cos^2 t / sin^2t * sint /1$

$= cos^2 t / sin^cancel2t * cancel (sint )/1$

$=cos^2 t /sint$

Use identity: $sin^2t+cos^2t=1$

$=(1-sin^2t)/sint$

$=1/sint - sin^2t / sint$

$=1/sint - sin^cancel 2t / cancel(sint)$

$=csct - sint$

$:.=$ Right Hand Side

How do you verify the identity cot^2t/csct=csct-sintcot^2t/csct=csct-sint?