Thread: C3 identity issue!

Can someone please direct me in the correct identities to use here, really stuck!

given that 5sec^2x + 3tan^2x =9, find the possible values of sin x.

Thanks!

Multiply through by then apply the Pythagorean identity to get a quadratic in .

Knowing that: tan^2x + 1 = sec^2x, sec^2x = 1/cos^2x and also sin^2x + cos^2x = 1, is what is required to answer this question.
More specifically begin by getting everything in terms of sin x and cos x and hopefully it will become much easier to manipulate.