(3) a sinθ + b cosθ = c .... (i) a cosθ – b sinθ = x (let) ... (ii) On squaring equations (i) and (ii) and adding, a2sin2θ+b2cos2θ+2absinθcosθ+a2cos2θ+b2sin2θ−2ab−sinθ.cosθ=c2+x2 ⇒a2(sin2θ+cos2θ)+b2(cos2θ+sin2θ)=c2+x2 ⇒a2+b2=c2+x2 ⇒x2=a2+b2−c2 ⇒x=±√a2+b2−c2