Question

Sin2a/cos2a + cos2a/sin2a = 1/sin2acos2a -2

Answer 1

sin²A/cos²A=(1-cos²A)/cos²A

=(1/cos²A)-(cos²A/cos²A)

=(1/cos²A)-1

Similarly we can prove that cos²A/sin²A = (1/sin²A)-1

∴ LHS = sin²A/cos²A + cos²A/sin²A =(1/cos²A)-1 + (1/sin²A)-1

= (1/sin²A + 1/cos²A) - 1

=(sin²A+cos²A)/sin²Acos²A - 2

=1/sin²Acos²A -2 =RHS

Hence proved