Question

If tana = xtanb then prove that sin(a-b)/sin(a+b) = x-1/x+1

Answer 1

tana = xtanb
sina/cosa = xsinb/cosb
sina.cosb/cosa.sinb = x/1

use componendo and dividendo rule ,
(sina.cosb + cosa.sinb)/(sina.cosb - cosa.sinb) = (x + 1)/(x - 1)

[ we know, sin(C ± D) = sinC.cosD±cosC.sinD]

so, sin(a + b)/sin(a - b) = (x + 1)/(x - 1)
hence, proved//

Answer 2

Hope this will help you..