count, \(cos\alpha \),when \(sin2\alpha =5/13\) ja \(-\frac\pi4\leq\alpha \geq\frac\pi4\)
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+130081 Sin (2A) = 5/13 ...... so ....Cos(2A) = 12/13
Using a half-angle identity
cos (A) = √ [ ( 1 + cos2A) / 2 ] = √ [ ( 1 + 12/13) / 2 ] =
√ [ (13 + 12) / 26 } = √ [ 25 / 26 ] = 5 / √26 =
(5/26)√26
And we take the positive root since the cosine is positive on the requested interval
