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**If tan2x=(-24/7), find the exact value(s) of sinx and cosx**

Working out the answers by hand, I get

sinx = ±3/5, ±4/5

cosx = ±3/5, ±4/5

But by actually calculating x and plugging it into sinx and cosx, I get

sinx = 3/5, 4/5

cosx = 3/5, -4/5

I'm pretty sure that the latter are the answers, but how do I justify it given the ±?