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a cos x+b sin x= c , divide both sides by(a^2+b^2)^1/2.
a/(a^2+b^2)^1/2.cos x+b/(a^2+b^2)^1/2.sin x=c/(a^2+b^2)^1/2.
Let a/(a^2+b^2)^1/2=sin A , then b/(a^2+b^2)^1/2=cosA
sinA.cos x+cos A.sin x=c/(a^2+b^2)^1/2
sin (A+x)= c/(a^2+b^2)^1/2
A+x=sin inverse c/(a^2+b^2)^1/2
x=sin inverse c/(a^2+b^2)^1/2-A
x=sin inverse c/(a^2+b^2)^1/2 - sin inverse a/(a^2+b^2)^1/2.
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