prove that

2tan-1 [ { (a-b) / (a+b) }1/2 tan x/2 ] = cos-1{ (b +acos x ) / (a+bcos x) }

let ..............(1)

let ..............(2)

 

from (1) and (3)

therefore

using equation (2)

thus

hope this helps you.

cheers!!

  • 32

RHS, apply the formula cosx= (1-tan2(x/2))/(1+tan2(x/2)). Then apply LCM.

So RHS =cos-1((a+b-(a-b)tan2(x/2))/(a+b+(a-b)tan2(x/2)))

Now for LHS apply the formula 2tan-1x=cos-1[(1-x2)/(1+x2)]

where x=[(a-b)/(a+b)]1/2tan(x/2)].

Take LCM again to get LHS=RHS

 

 

  • 14
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