Question

given 3 tan a tan b =1, then prove 2 cos (a+b) =cos (a-b)

Answer 1

3.tana .tanb = 1
3sina. sinb/cosa.cosb = 1
sina.sinb/cosa.cosb = 1/3

use, componendo dividendo rule ,

(sina.sinb + cosa.cosb)/(cosa.cosb - sina.sinb) = (1 + 3)/(3 -1)
[ use, cosa.cosb+ sina.sinb = cos(a -b)
cosa.cosb - sina.sinb = cos(a + b) ]

cos( a - b)/cos(a + b) = 4/2 = 2

cos(a - b) = 2cos(a + b)
hence proved //

Answer 2

Answer:

Step-by-step explanation: