Question

How can we prove that tan70=tan20+2tan50

Answer 1

using tan(x-y)=(tan x- tan y)/1+tan x .tan y ,we get tan(x-y).(1+tan x .tan y)=tan x -tan y

Hence for x=70°&y=20° we get

tan 50°.(1+tan 70° .tan 20°)=tan70°-tan20°
But tan A=cot(90°-A), implying tan20°=cot70°

Hence tan50°.(1+tan70° .cot70°)=tan70°-tan20°
tan50°.(1+1)=tan 70°-tan20°

2tan50° = tan70°- tan20°