Originally Posted by

**HumanShale** I approached it this way:

1.) tan x = 3sin x

2.) sin x / cos x = 3sin x

3.) sin x = 3sin x cos x

4.) sin x = 3sin x (sqrt(1 - sin^2 x))

5.) 1 = 3(sqrt(1 - sin^2 x))

6.) 1 = 9(1 - sin^2 x)

7.) 9 -9sin^2 x = 1

8.) -9sin^2 x = -8

9.) sin^2 x = 8/9

10.) sin x = sqrt(8/9)

This gives me solutions in radians at approx: 1.23, 1.91, 5.05, 4.37

The original equation (ignoring solutions at 0, pi, 2pi) has only 2 solutions at: 1.23 and 5.05.

I've drawn graphs at various stages and I start getting 4 solutions at step 4.

What am I doing wrong here?

Thanks.