Question

If sinx + siny = 2sin(x+y) then show that tanx/2 tany/2 = 1/3

Answer 1

Answer:

Step-by-step explanation:

Formula: sinA + sinB = 2sin(A+B)/2cos(A-B)/2

         and sinA = 2sin(A/2)cos(A/2)

Given sinx + siny = 2sin(x+y),

=>2sin(x+y)/2cos(x-y)/2 = 2*2sin(x+y)/2cos(x+y)/2

=>cos(x-y)/2 = 2cos(x+y)/2

cos(x/2)cos(y/2) + sin(x/2)sin(y/2) =2( cos(x/2)cos(y/2) - sin(x/2)sin(y/2))

=>3 sin(x/2)sin(y/2) = cos(x/2)cos(y/2)

Dividing by cos(x/2)cos(y/2) on both sides, we get

Hence, tanx/2 tany/2 = 1/3