Question

How do you verify `(1-tan^2x) / (1+tan^2x) = 1-2sin^2`?

Answer 1

`L.H.S=R.H.S`

Explanation:

`L.H.S = (1-tan^2x)/(1+tan^2x)`
`=(1-sin^2x/cos^2x)/(1+sin^2x/cos^2x`
`=((cos^2x-sin^2x)/cos^2x)/((cos^2x+sin^2x)/cos^2x)`
`=(cos^2x-sin^2x)/(cos^2x+sin^2x)`
`=(cos^2x-sin^2x)/1 ; Since cos^2x+sin^2x=1;cos^2x=1-sin^2x`
`=cos^2x-sin^2x`
`=1-sin^2x-sin^2x`
`=1-2sin^2x`
`=R.H.S`