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43 votes

cos^(2) ((1)/(2)*arccos(-(12)/(13) ))

User Gustavo Gabriel
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1 Answer

12 votes
12 votes

Recall the half-angle identity,

cos²(x/2) = (1 + cos(x))/2

This means


\cos^2\left(\frac12 \arccos\left(-(12)/(13)\right)\right) = \frac{1 + \cos\left(\arccos\left(-(12)/(13)\right)\right)}2 = \frac{1 - (12)/(13)}2 = \boxed{\frac1{26}}

User Alexey Semenyuk
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