I need to verify this question to make the identities match
2 - tan^2 x = 3 - sec ^2 x
Subtract 2 from both sides of equation.
- tan^2 x = 1 - sec^2 x
Add sec^2 x to both sides of equation.
sec^2 x - tan^2 x = 1
sec x = (1 / cos x). tan x = (sin x / cos x). 1 = (cos x / cos x).
(1 / cos^2 x) - (sin^2 x / cos^2 x) = (cos^2 x / cos^2 x)
All denominators are now equal, so they can be dropped.
1 - sin^2 x = cos^2 x
1 = sin^2 x + cos^2 x