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sint/csct = 1-cost/sect

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Cheahjimmyviz
LHS      sin t/csc t = sin t/(1/sin t)  = sin² t
RHS      1- cos t/sec t =  1- cost/1/cos t =  1 - cos² t
so      sin² t = 1 - cos² t      /  sin² t + cos² t = 1
we have proven that
sin² t = 1- cos² t  is true
thus this is an identity