Question

Complete the statements.

Answer 1

Answer:

1. 30

2. 150

Step-by-step explanation:

$3tan^2(x)-1 =0$

Lets assume tan(x) = u

$3u^2(x)-1 =0$

Now we solve for 'u'

add 1 on both sides

$3u^2(x) =1$, divide both sides by 3

$u^2 = \frac{1}{3}$

Take square root on both sides

$u = +-\frac{1}{\sqrt{3} }$

We replace tan(x) for 'u'

$tan(x) = +-\frac{1}{\sqrt{3} }$  

x = 30 because $tan(30) =+\frac{1}{\sqrt{3} }$  in first quadrant

      x = 30      (tan is positive in first quadrant)

$tan(x) =-\frac{1}{\sqrt{3} }$                                                    

  x = 150 because $tan(150) =-\frac{1}{\sqrt{3} }$  in second quadrant

     tan is negative in second quadrant