Verify the identity:
(1 + tan^2x)(1 - sin^2x) = 1

i know the solution, but not the steps to get me the answers i need. i will need to know how to do this on my own for a test soon, so any explanations will be appreciated.

solution, kinda: (1 + tan^2x)(1 - sin^2x) = sex^2x * cos^2x = 1/cos^2x = 1

here are some identities that i'm pretty sure need to be used, but i'm not sure how or in what context to use them.

quotient identities:
tan x = (sin x)/(cos x)
cot x = (cos x)/(sin x)

reciprocal identities:
csc x = 1/(sin x)
sec x = 1/(cos x)
cot x = 1/(tan x)

pythagorean identities:
sin^2x + cos^2x = 1
sec^2x = 1 + tan^2x
csc^2x = 1 + cot^2x

any and all will be greatly appreciated!