IIT JEE , AIEEE Forum - Mathematics , Trignometry

rtiit

Find value of k in terms of m

If cosA=mcosB

and

sagarvaze

is it m+1/m-1

rtiit

plz give detailed soln yar

sagarvaze

k=1/(tan(A+B/2)tan(B-A/2)
   = cos(A+B/2)cos(A-B/2)/sin(A+B/2)sin(B-A/2)
   = 2cos(A+B/2)cos(A-B/2)/2sin(A+B/2)sin(B-A/2)
   = cosA+cosB/cosA-cosB
   = (m+1)/(m-1)

sunip_the_mini_mastermind

in the first given eqn...take cosB in the denominator ...then apply componenedo and dividendo...apply which u will get a eqn like the second one...

ramkumar_november

$m=\frac{cosA}{cosB}$

$\frac{m+1}{m-1}=\frac{cosA+cosB}{cosA-cosB}$

$\frac{m+1}{m-1}=\frac{2cos\bigg(\frac{A+B}{2}\bigg)cos\bigg(\frac{A-B}{2}\bigg)}{2sin\bigg(\frac{B-A}{2}\bigg)sin\bigg(\frac{A+B}{2}\bigg)}$

$\frac{m+1}{m-1}=\frac{cot\bigg(\frac{A+B}{2}\bigg)}{tan\bigg(\frac{B-A}{2}\bigg)}$

$\frac{m+1}{m-1}=K$

rtiit

@sagar
here r ur ratez........

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