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Writing x instead of theta, cos2x = 1 - (12/13)2 = 1 - 144/169 = 25/169 = (5/13)2

So cos(x) = ± 5/13

so that x = cos-1(5/13) or cos-1(-5/13)

And then, depending on the range of x, you have solutions for x. A calculator will only give you the principal solutions, though.

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Q: How do you calculate cos squared theta equals one minus twelve thirteenths squared?
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