Use the trigonometric identities:
\(\sec x= \frac{1}{\cos x} \\
\tan x= \frac{\sin x}{\cos x} \\
\sin^2 x+ \cos^2 x=1\)
\(\sec^2 x-1=\tan^2 x \\
(\frac{1}{\cos x})^2-1=(\frac{\sin x}{\cos x})^2 \\
\frac{1}{\cos^2 x}-1 = \frac{\sin^2 x }{\cos^2 x} \ \ \ |\times \cos^2 x \\
1-\cos^2 x=\sin^2 x \ \ \ |+\cos^2 x \\
\sin^2x+\cos^2x=1 \\ \boxed{\hbox{true}}\)
