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Solve:
6sin square x - sinxcosx - cos square x =3
use cos^2(x) =(1+cos2x)/2 sin^2(x) =(1-cos2x)/2 and sinxcosx = sin(2x)/2, solve the resulting equation for 2x and then divide by 2 to get x
6sin2x-sinx.cosx-cos2x = 3
multiplying 2 on both sides we get
12sin2x-2sinx.cosx-2cos2x = 6
but we know that cos2x=1-sin2x and 2sinx.cosx=sin2x
12sin2x-sin2x-2(1-sin2x) = 6
12sin2x-sin2x-2+2sin2x = 6
14sin2x-sin2x = 6+2 = 8
further simplify
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