3 tan^2 7x = 1

Question

How many answers would you expect this equation to have on [0,2π)? Explain why.

Answer 1

3tan²7x = 1; 3(1 - cos14x)/(1 + cos14x) = 1; 3 - 3cos14x = 1 + cos14x; cos14x = 1/2;

So we have 28 solutions on interval [0, 2π)

Answer 2

3 tan^2 7x = 1

" " " = 1/3

tan 7x = .5773.....

" " = 30

x = 4.285....