SOLUTION: Good morning! Alas... in need of help on a very simple problem. tan^2(3x) = 3 I am unsure of where exactly to start on this problem. Have applied the trig identity for tan^2(x

Algebra ->  Trigonometry-basics -> SOLUTION: Good morning! Alas... in need of help on a very simple problem. tan^2(3x) = 3 I am unsure of where exactly to start on this problem. Have applied the trig identity for tan^2(x      Log On


   

Question 439483: Good morning!
Alas... in need of help on a very simple problem.
tan^2(3x) = 3
I am unsure of where exactly to start on this problem. Have applied the trig identity for tan^2(x) which is (1-cos2x)/(1+cos2x) but am not sure if that is the correct way to go. Please break down and explain!
Thank you!
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
%28tan%283x%29%29%5E2=3 is a trigonometric equation.Taking the square root of both
sides of the equation, we have two equivalent equations:
tan%283x%29=sqrt%283%29,(1) and, tan%283x%29=-sqrt%283%29, (2).
As you know the function tan(x) is periodic function with period pi.
Solving each of them we have:3x=n%2Api%2B%28pi%29%2F3=> x=n%2Api%2B%28pi%29%2F9 and
x=n%2Api%2B%284%2Api%29%2F9, for equation (1).
3x=n%2Api-%28pi%29%2F3 => x=n%2Api-%28pi%29%2F9 and x=n%2Api-%282%2Api%29%2F9
for equation (2)