If acosx-bsinx =c, prove that asinx + bcosx = +- root(a2+b2-c2)

a cosx - b sinx = c

a2 cos2x + b2 sin2x - 2ab sinx cosx = c2

a2 ( 1 - sin2x) + b2 ( 1 - cos2x) - 2ab sinx cosx = c2

a2 - a2 sin2x + b2 - b2 cos2x - 2ab sinx cosx = c2

-(a2 sin2x + b2 cos2x + 2ab sinx cosx) = -a2 - b2 + c2

(a sinx + b cosx)2 = a2 + b2 - c2

asinx + bcosx = +- root(a2+b2-c2)

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