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Ut is equual to tan(theta) / (sec(theta) + 1)
It also equals 13 12.
For such simplifications, it is usually convenient to convert any trigonometric function that is not sine or cosine, into sine or cosine. In this case, you have: sin theta / sec theta = sin theta / (1/cos theta) = sin theta cos theta.
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If sine theta is 0.28, then theta is 16.26 degrees. Cosine 2 theta, then, is 0.8432