Question

cos^2x(sec^2x-1)

Answer 1

\(\sec x:=\dfrac1{\cos x}\) (\(:=\)means "is defined to be")

Answer 2

\[cos^2x(\sec^2x-1)\]\[=cos^2x(\dfrac1{\cos^2x}-1)\]\[=1-\cos^2x\]\[=sin^2x\]

Answer 3

^@kc he explained it all; at the very end, he used an identity.