Question

Prove that 1+ cot²A/1+cosecA = cosecA

Answer 1

Hi ,

LHS = 1 + cot²A/( 1 + cosecA )

= 1 + [cot²A(cosecA-1)/(cosecA+1)(cosecA-1)]

= 1 + [ cot²A(cosecA-1)/( cosec²A - 1²)]

= 1 + [ cot²A( cosecA - 1 )/cot²A]

[ Since cosec²A - 1 = cot²A ]

= 1 + cosecA - 1

= cosecA

= RHS

I hope this helps you.

: )