# trig

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If cscx=2 and x greater 90 degrees and x less than 180 degrees, then sin x/2 =

• trig -

So sinx = 1/2 and x must be in 2nd quadrant.
then by Pythagoras cos x = -√3/2

we know cos 2A = 1 - 2sin^2A
then cosx = 1 - 2sin^2(x/2)
-√3/2 = 1 - 2sin^2(x/2)
2sin^2(x/2) = 1 + √3/2
sin^2(x/2) = (2 + √3)/4
sin(x/2) = (√(2+√3))/2

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