Question

How do you prove `1+cos2x=2/(1+tan^2x)` using the double angle identity?

Answer 1

`cos 2x = 2cos^2x - 1`
`tan^2 x + 1 = sec^2 x`

`1 + cos 2x = 2 cos^2 x = 2/sec^2 x = 2/(1 + tan^2 x)`