Question

Verify the identity.
(1 − sin^2 x)(tan^2 x + 1) = 1

Use the Pythagorean and Reciprocal Identities, and simplify.

(1-sin^2 x)(tan^2 x1) = (?)(sec^2 x)
= (?)(1/cos^2 x)
= (?)

Answer 1

Recall
\[1-\sin^2(x)=\cos^2(x)\]

Answer 2

(1-sin^x) = cos^2x
tan^2x+1 = 1/cos^x

Product of those two = 1.

Answer 3

tan^2x+1 = 1/cos^2x I meant.