Question

How do I prove this trig equation? I have to substitute identities to match the left side of the equation to the right.

1 + sec²x sin²x = sec²x

Answer 1

If you turn sec^2x into 1/cos^2x, you'd end up with:
1+(sin^2 x)/(cos^2 x) = sec^2 x.
Now, sinx/cosx=tanx, so now you have:
1+tan^2 x=sec^2 x, and that is an identity.

Answer 2

Thanks so much! I was spending way too long on this problem.

Answer 3

No problem!