Question

If x=cosecA +cosA and y = cosec A - cosA then prove that (2/x+y)square + (x-y/2)square - 1 =0

Answer 1

x = cosec A + cos A                y = cosec A - cos A
=>  x+y = 2 cosec A
=>  2/(x+y) = sinA 

(x - y)/2 =  cos A

LHS = [ 2/(x+y) ]² + [(x-y)/2]²  - 1
        = sin² A + cos ² A - 1  
         = 1 - 1 = 0

Answer 2

ANSWER IS IN THE ATTACHMENT