Question

True or false: The equation sec^2 x - 1 = tan^2 x is an identity.

Answer 1

True

Explanation:

Answer 2

Use the trigonometric identities:

`\sec x= (1)/(\cos x) \\ \tan x= (\sin x)/(\cos x) \\ \sin^2 x+ \cos^2 x=1`


`\sec^2 x-1=\tan^2 x \\ ((1)/(\cos x))^2-1=((\sin x)/(\cos x))^2 \\ (1)/(\cos^2 x)-1 = (\sin^2 x )/(\cos^2 x) \ \ \ |* \cos^2 x \\ 1-\cos^2 x=\sin^2 x \ \ \ |+\cos^2 x \\ \sin^2x+\cos^2x=1 \\ \boxed{\hbox{true}}`