Question

if tan(A+B)= x and tanB=1/2 prove that tanA= 2x-1/x+2​

Answer 1

ANSWER:

tan(A+B) = (tanA + tanB)/(1 - tanAtanB)

given,

tan(A+B) = x & tanB = 1/2.

hence,

x = (tanA + 1/2)/(1 - (tanA)/2)

x - (x/2)tanA = tanA + 1/2

tanA + (x/2)tanA = x - 1/2

tanA (1 + x/2) = x - 1/2

tanA = ((2x - 1)/2)×(2/(x + 2))

tanA = (2x - 1)/(x + 2)