1.

cos A -sin A + 1cA Cosec A + cot A, using the identity cosec A-1+ cot A.

Answer»

LHS:Cos A - Sin A + 1/ Cos A + Sin A - 1 dividing in numerator & denominator with Sin ACot A - 1 + Cosec A / Cot A - Cosec A + 1now putting 1= Cosec^2 - Cot ^2

= (Cot A + Cosec A) - (Cosec^2 A - Cot^2 A) / (Cot A - Cosec A + 1)

= (Cot A + Cosec A) [1 - Cosec A + Cot A) / (Cot A - Cosec A + 1)]

= (Cot A + Cosec A)

= RHS

Hence Proved



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