1.

(cosec*theta %2B cot(theta) - 1)/(-cosec*theta %2B cot(theta) %2B 1)=cosec*theta %2B cot(theta)

Answer»

Let theta = x

LHS: (cotx+cosecx)-1/(cotx-cosecx+1)

=(cosecx+cotx)-(cosec²x-cot²x)/(cotx-cosecx+1)

= (cosecx+cotx)[1-(cosecx-cotx)]/(cotx-cosecx+1)

= (cosecx+cotx)(cotx-cosecx+1)/(cotx-cosecx+1)

= (cosecx+cotx)

= RHS

Hence proved



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