Question

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

Answer 1

so, what is the question? is it to prove equality?

Answer 2

if so
\[2-\frac{ \sin ^2}{ \cos^2 }=3-\frac{ 1 }{ \cos^2 }\]
the you multiply by cos^2 and you get
\[2\cos^2-\sin^2=3*\cos^2-1\]
remember sin^2=1-cos^2 so
\[2*\cos^2-1+\cos^2=3*\cos^2-1\]
so they are equall

Answer 3

Generally when a problem asks us to `verify` something, they want you to leave one side untouched, and manipulate the other side so that both sides match. So while Sanjar's steps look correct, it's not the process we want to take I'm afraid. :)

Let's use this important identity to verify this problem.\[\large \color{cornflowerblue}{1+\tan^2x=\sec^2x}\]

Let's leave the right side alone, and manipulate the left side to match it! :)
\[\large 2-\tan^2x=3-(\color{cornflowerblue}{\sec^2x})\]
We'll use our identity to substitute in it's equivalent.\[\large 2-\tan^2x=3-(\color{cornflowerblue}{1+\tan^2x})\]
From here, just distribute the negative to each term in the brackets, and it shouldn't take much more than that to match them up! :)

Answer 4

Sorry I spoke backwards ~ We kept the Left side the same, and manipulated the Right side.*