Question Number 114100 by faysal last updated on 17/Sep/20

  If cos =((acos α−b)/(a−bcos α)), prove that,  ((tan (1/2)θ)/( (√(a+b))))=((tan (1/2)α)/( (√(a+b))))

Commented byHenri Boucatchou last updated on 17/Sep/20

cos?=((acosα....)/)

Commented bysom(math1967) last updated on 17/Sep/20

I think it should be cosθ

Answered by som(math1967) last updated on 17/Sep/20

(1/(cosθ))=((a−bcosα)/(acosα−b))  ((1+cosθ)/(1−cosθ))=((a−b+(a−b)cosα)/((a+b)−(a+b)cosα))  [using componendo and dividendo]  (1/(tan^2 (θ/2)))=(((a−b)(1+cosα))/((a+b)(1−cosα)))  tan^2 (θ/2)=(((a+b))/((a−b)))tan^2 (α/2)  tan(θ/2)=(√((a+b)/(a−b)))tan(α/2)  ((tan(θ/2))/( (√(a+b))))=((tan(α/2))/( (√(a−b)))) (proved)