Question

Please simplify the expression to either a constant or a basic trigonometric function.

(sec^2x+csc^2x)-(tan^2x + cot^2x)

Answer 1

are these sec, csc, tan, and cot squared of x?
if so then you can use pythagoran identities to simplify the expression and get like terms to manipulate. such as\[\sec ^2(x)=\tan ^2(x)+1 or 1+\cot ^2(x) = \csc ^2(x)\] it also helps to know what this is all equal too. but you could substitue wither one of those equations to get like terms and get an easy answer.

Answer 2

no they are not square of x

Answer 3

so the eq. is not \[(\sec^2(x)-\csc^2(x))-(\tan^2(x) + \cot^2(x))\]? Use those pythag ID's to put the eq in either tan &cot, or sec & csc. Otherwise your best bet is to make all of the terms in sin and cos, that won't really get you much further though especially without an equivalent value. If it is like I wrote it, then \[-2\cot^2(x) \] is a simpler expression