Question 293364
find the exact value of cos(arcsin(-1/2) + arctan(2/3))
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Plot the points and assign the angles A and B
A = arcsin(-1/2) = -30º
cos(A) = sqrt(3)/2
sin(A) = -1/2
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B = arctan(2/3) 
gives the point (2,3), a distance of sqrt(13) from the Origin.
cos(B) = 3sqrt(13)/13
sin(B) = 2sqrt(13)/13
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cos(A+B) = cos(A)cos(B) - sin(A)sin(B)
= sqrt(3)/2 * 3sqrt(13)/13 - (-1/2)*2sqrt(13)/13
= {{{3sqrt(39)/26 + sqrt(13)/13}}}
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or, = {{{(sqrt(13)/26)*(3sqrt(3) + 2)}}}