To solve the equation, we'll replace tan x by
t:
The equivalent equation
is:
t^2 - 18t + 72 = 0
We'll
apply quadratic formula to find the roots:
t1 =
[18+sqrt(324 - 288)]/2
t1 =
(18+6)/2
t1 = 24/2
t1 =
12
t2 = (18-6)/2
t2 =
6
But tan x = t1 => tan x = 12 => x1 = arctan
12 + k*pi
tan x = t2 => tan x = 6 => x2 =
arctan 6 + k*pi
The solutions of the equation
belong to the reunion of sets: {arctan 6 + k*pi}U{arctan 12 +
k*pi}.
No comments:
Post a Comment