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Given cos x = -3/5 , sin y =12/13 and 0º< x <360º,x and y are on the same quadrant. Without using mathematical table and scientific calculator,find the values for:
(a)sin 1/2 x
(b)cos (x+y)

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  1. since cosx < 0 and siny > 0, and both x and y are in the same quadrants, the angles must be in II

    if cosx = -3/5, then sinx = 4/5
    if siny = 12/13, then cosy = - 5/13

    a) from cos 2A = 1 - 2 cos^2 A
    cos x = 1 - 2 sin^2 (x/2)
    -3/5 = 1 - 2sin^2 (x/2)
    2sin^2 (x/2) = 1 + 3/5 = 8/5
    sin^2 (x/2) = 4/5
    sin (x/2) = 2/√5

    b)
    cos(x+y) = cosxcosy - sinxsiny
    = sub in the above values and simplify

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