2-tan^2 x=3-sec^2 x

Question

I need to verify this question to make the identities match

Answer 1

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