Hi my name is Alex I am a fresman in college and I am in Trig. I really need help with proving this identity. I know I have to multiply the left side by either the congugate of the numerator or the congugate of the denominator, I get almost to the end but then I end up with a sign error. Please help it is driving me nuts. Thank you so much.

I don't think that the conjugate will work well here. I would multiply both sides by the denominator, 1 + cosx - sinx. Also write secx as  ¹/_cosx and tanx as  ^sinx/_cosx, and then multiply both sides by cosx. This will clear all the denominators.

Now expand each side and simplify, rembering that 1 - sin²x = cos²x.

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