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Let `L` denots value of `cos^(2)(alpha - beta)` if `sin2alpha + sin2beta = (1)/(2), cos2alpha + cos2beta = (sqrt(3))/(2)` and `M` denotes value of `(1)/(log_(xy)xyz) + (1)/(log_(yz)xyz) + (1)/(log_(zx)xyz)` then `16L^(2) + M^(2)` is |
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Answer» Correct Answer - 5 `1 + 1 + 2cos2(alpha - beta) = (1)/(4) + (3)/(4) = 1` `2 + 2(2cos^(2)(alpha - beta) - 1) = 1` `cos^(2)(alpha - beta) = (1)/(4) = L rArr L = (1)/(4)` `m = log_(xyz)xy + log_(xyz)yz + log_(xyz)(xyz)^(2) = 2` `:. 16L^(2) + m^(2) = 1 + 4 = 5` |
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