Use basic identities to simplify the following expression.
tan^2x-sec^2x/cosx
To simplify the expression tan^2x - sec^2x / cosx, we first need to rewrite sec^2x in terms of sin and cos:
sec^2x = 1/cos^2x
sec^2x = 1 + tan^2x
Now, substitute this into the expression:
tan^2x - (1 + tan^2x) / cosx
= tan^2x - 1 - tan^2x / cosx
= -1 / cosx
= -secx
Therefore, the simplified expression is -secx.