If cos theta = cos A-cos B/1-cosAcosB prove that one of the values of tan theta/2 is tan A/2. cotB/2?

Answer 1

GOOD QUESTION
WHERE DID U GET IT FROM
sorry couldn't solve it
i did try to but couldn't

Answer 2

RD Sharma pg 9.27

Answer 3

i think first use the formula cos(θ/2)= sqrt[(1+cos θ)/2]
and then covert it into sec(θ/2) and use
sec(θ/2)^2 - 1 = tan(θ/2)^2
but i have reached till
tan(θ/2) =
sqrt [(1+cosAcosB-cosA+cosB) / (1-cosAcosB+cosA-cosB)]
if only i could simplify. u can try by using cosA=2cos(a/2)^2 - 1

Answer 4

good question.
I have considered question as: cos x=(cosA-cosB)/(1-cosAcosB)
cos x=[1-tan^2(x/2)]/[1+tan^2(x/2)]
by componendo-dividendo on LHS andRHS
[(-1)/tan^2(x/2)]=
[(cosA-cosB+1-cosAcosB)/(cosA-cosB-1+cosAcosB)]
factorising numerator and denominator of RHS
[(-1)/tan^2(x/2)]=
[{(1+cosA)(1-cosB)}/{(cosA-1)(1+cosB)}]=
[{cos^2(A/2)sin^2(B/2)}/{-sin^2(A/2)cos^2(B/2)}]=
{-cot^2(a/2)tan^2(B/2)}
cancelling negative sign on both sides and taking reciprocal we get required result.

Answer 5

hey first tell me that it is (cos A- cos B)/ (1-cosA cos B) or it is cos A - (cos B/ (1- cos A cos B))?? it is very confusing here! please be specific!