Question

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

Answer 1

See explanation...

Explanation:

Use:

`sec x = 1/cos x`

`tan x = sin x / cos x`

`cos^2 x + sin^2 x = 1`

Then:

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

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

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

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