Question

1+cos2A/sin2A = 2cos2A​

Answer 1

Well we know that for two angles A,B it holds that

cos(A+B)=cosAcosB−sinA⋅sinB

hence for A=B you get

cos(2A)=cos2A−sin2A

But sin2A=1−cos2A

hence

cos(2A)=cos2A−(1−cos2A)=2cos2A−1