Question

If tan 2x =2 for 0 < x < 90 , determine the exact value of tan x !

Answer 1

\[Tan((Tan^{-1}2)\div2)\]

Answer 2

tan 2x = \(\dfrac{2tanx}{1-tan^2x}=2\) \(\rightarrow 2tanx = 2(1-tan^2x)=2-2tan^2x\)
so, tan^2 +tan x -1 =0
solve as a quadratic by let tan x =t, you have t^2 +t -1 =0
after solving for t, plug back to get tan x

Answer 3

ok, thanks

Answer 4

np