Question

if b cos€=a,then prove that cosec€ +cot€=√b+a÷b-a

Answer 1

let €=A.
Then, by the question,
b cosA=a=>b+a/b-a=secA+1/secA-1
(by componendo and dividendo)
Then, b+a/b-a=1+cosA/1-cosA
=>√(b+a/b-a)=cot(A/2)...by formula of submultiples.
we need to prove that (1+cosA)/sinA=√(b+a/b-a)
now by the formula, 1+cosA=2cos²(A/2)
and sinA= 2sin(A/2)cos(A/2).
substituting we get, cot(A/2)=√(b+a/b-a).