Question

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

Answer 1

x = cosecA+cosA

y = cosecA-cosA

To prove: (2/x+y)^2 + (x-y/2)^2  - 1 =0

x+y = 2cosecA

x-y= 2cosA

Thus (2/2cosecA)^2 + (2cosA/2) - 1

= (1/cosecA)^2 + (cos A)^2 - 1

=sin^2 A + cos^2 A - 1

= 1 - 1

= 0

Thus, LHS=RHS

{ Points to remember:

sin = 1/cosec

sin^2 + cos^2 = 1 }