Question

acos x-bsin x=c,prove that a sinx +b cos x=root a^2+b^2+-c^2

Answer 1

Hey,here your answer,
(acosx-bsinx) =x
=(acosx-bsinx) ^2+(asinx+bcosx) ^2
=a^2cos^2+b^2sin^2-2asinx*coax+a^2sin^2+b^2sin^2x+2sinx*cosx
=a^2(sin^2+cos^2)+b^2(sin^2+cos^2)
=a^2+b^2
Thus,
(acosx-bsinx) ^2+(asinx+bcosx) ^2
=c^2+(asinxx+bcosx)^2=a^2+b^2
=(asinx+bcosx)^2=a^2+b^2-c^2
(asinx+bcosx) =√a^2+b^2-c^2