Question

If a cos A-b sin A = c, prove that a sin A +b cos A = +- underoot(a^2+b^2-c^2)​

Answer 1

a cosA - b sinA = c

a2 cos2xA+ b2 sin2A - 2ab sinA cosA = c2

a2 ( 1 - sin2A) + b2 ( 1 - cos2A) - 2ab sinA cosA = c2

a2 - a2 sin2A + b2 - b2 cos2A - 2ab sinA cosA = c2

-(a2 sin2A + b2 cos2A + 2ab sinA cosA) = -a2 - b2 + c2

(a sinA + b cosA)2 = a2 + b2 - c2

asinA + bcosA = +- √(a2+b2-c2)

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