Question

If cos[theta +2 alpha ]=m cos theta ,prove that cot alpha =1+m/1-m tan [theta + alpha .

Answer 1

this is the answer for your questions

Answer 2

the given equation is: cos(θ+2α)=m.cosθ ....(1)

⇒1m=cosθcos(θ+2α)applying componendo and dividendo:1+m1−m=cosθ+cos(θ+2α)cosθ−cos(θ+2α)1+m1−m=2cosθ+(θ+2α)2.cosθ−(θ+2α)22sinθ+(θ+2α)2.sin(θ+2α)−θ21+m1−m=cos(θ+α).cosαsin(θ+α).sinα1+m1−m*sin(θ+α)cos(θ+α)=cosαsinα

⇒1+m1−m*tan(θ+α)=cotα

hope this helps you