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
