Hello.
I am trying to simplify the problem, (tan^2x-sec^2x)/cosx, but I am unsure how. Does anyone have any formulas or starting moves for me to begin to simplify this problem, using basic identities?
Sure, I can help! Let's start by using the identity:
tan^2x + 1 = sec^2x
Using this identity, we can rewrite the numerator as:
tan^2x - sec^2x = tan^2x - (tan^2x + 1) = -1
So now our expression becomes:
-1/cosx
We can further simplify this by using the identity:
secx = 1/cosx
Therefore, our final simplified expression is:
-secx
takes 3 steps:
(tan^2x-sec^2x)/cosx
= (sec^2 x - 1 - sec^2 x)/cos x
= -1/cosx
= -secx
or, if you are not familiar with the identity used, often just changing
everything to sines and cosines will work:
(tan^2x-sec^2x)/cosx
( sin^2 x/cos^2 x - 1/cos^2 x) / cosx
= ( (sin^2 x - 1)/cos^2 x )/cosx
= - cos^2 x / cos^3 x
= -1/cosx
= -secx