Verify: cot(x/2) - cotx = cscx

... LHS

= [ cot (x/2) ] - cot x

= ( cos x/2 / sin x/2 ) - ( cos x / sin x )

= ( sin x cos x/2 - cos x sin x/2 ) / ( sin x/2 sin x )

= [ sin (x - x/2) ] / ( sin x/2 sin x )

= ( sin x/2 ) / ( sin x/2 sin x )

= 1 / ( sin x )

= csc x

= RHS
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