FIND
Asked by | 17th Sep, 2008, 07:40: PM
x lies in third quadrant means pi ≤ x ≤3*pi/2
sinx = -4/5 (since sin is negative in this range)
then pi/2≤ x/2 ≤3*pi/4 and 2*pi≤ 2x ≤3*pi
we know that |cos x| = 2cos2 x/2 -1 => cos(x/2) = 2/5
but since pi/2≤ x/2 ≤3*pi/4 in that range cos is negative cos(x/2) = -2/5
similarly sin is positive in both the range sin(x/2) = 1/5
and sin2x = 2 sinx cos x = 2(-3/5)(-4/5) = 24/25
Answered by | 18th Sep, 2008, 12:47: PM
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