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Oops, accidently hit enter. Cos2x=cos^2x-sin^2x Also cos2x=2cos^2x-1. And cos^2x=1-2sin^2x Set the second two both equal to 1/9, should get cosx=square root of 5/9 and sinx=2/3. Substitute answers back into first equation to check answers. 1/9= 5/9-4/9
How is that correct? The cos of cos2x cannot just disappear, you'd have to take the cosine inverse to get rid of it. So to solve for x, it would be
cos^-1 (cos2x)=cos^-1 (1/9)
But the problem can easily be solved without a calculator using double angle identities, so why not just do it that way and get "nice" numbers?