Let α be an acute angle such that cos α = 3/5 , and let β be an obtuse angle such that sin β = 5/13. Compute cos(α − β).
sin a = sqrt [ 5^2 - 3^2 ] / 5 = sqrt [ 16 ] / 5 = 4/5
cos B = - sqrt [ 13^2 - 5^2 ] / 13 = - sqrt [ 144 ] / 13 = - 12/13
cos ( a - B) =
cos(a)cos(B) + sin (a) sin (B) = (3/5) (-12/13) + (4/5)(5/13) =
(-36 / 65) + (20 / 65) =
-16 / 65
thank you so much!!
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