Question 734834
cos(A) = 1/3


cos^2(A) = (1/3)^2


cos^2(A) = 1/9


1 - cos^2(A) = 1 - 1/9


sin^2(A) = 8/9


sin(A) = sqrt(8/9)


sin(A) = sqrt(8)/3 ... angle A is in quadrant I, so sin(A) is positive


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sin(B) = -1/4


sin^2(B) = (-1/4)^2


sin^2(B) = 1/16


1 - sin^2(B) = 1 - 1/16


1 - sin^2(B) = 15/16


cos^2(B) = 15/16


cos(B) = sqrt(15/16)


cos(B) = sqrt(15)/4 ... angle B is in quadrant IV, so cos(B) is positive



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cos(A+B) = cos(A)cos(B) - sin(A)sin(B)


cos(A+B) = (1/3)(sqrt(15)/4) - (sqrt(8)/3)(-1/4)


cos(A+B) = sqrt(15)/12 + sqrt(8)/12


cos(A+B) = ( sqrt(15) + sqrt(8) )/12


So {{{cos(A+B) = ( sqrt(15) + sqrt(8) )/12}}}