Question

If A and β are the roots of acosx + bsinx = c then show that cos( A– β ) = ( 2c^2-(a^2+b^2))/a^2+b^2

Answer 1

so sorry I do not know it.

Answer 2

hoi mate here's your answer

Cos(α+β)=cosα∗cosβ−sinα∗sinβ

acosθ+bsinθ=c

acosθ=c−bsinθ

Square both sides

a2(1−sinθ)=c2+b2sin2θ−2∗c∗b∗sinθ

(b2+a2)sin2θ−2∗c∗b∗sinθ+c2−a2=0

Product of Roots =ca

sinα∗sinβ=c2−a2a2+b2

Now use similar method to have an equation in terms of cos2θ

acosθ+bsinθ=c

acosθ−c=−bsinθ

a2cos2θ+c2−2∗a∗ccosθ=b2(1−cos2θ)

(a2+b2)cos2θ−2∗a∗cosθ∗c+c2−b2=0

Product of Roots =ca

cosα∗cosβ=c2−b2a2+b2

Now substitute the values in First Equation 

cos(α+β)=cosα∗cosβ−sinα∗sinβ

⟹c2−b2+a2−c2a2+b2

⟹a2−b2a2+b2

hoped it helped you

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