How do I simplify this using trig identities?

Question

-sec²(-x)+ sin²(-x)+ cos²(-x)

Answer 1

cosx and secx are even functions and sinx is an odd function, so cos(-x) = cosx, sec(-x) = secx and

sin(-x) = -sinx

So, the given expression can be rewritten as:

-sec²x + sin²x + cos²x

= -sec²x + 1 (because cos²x + sin²x = 1)

= -tan²x (because 1 + tan²x = sec²x)