Question

Complete the statements.

1.The solution of 3tan2x − 1 = 0 if x is in the first quadrant is °.
2. The solution of 3tan2x − 1 = 0 if x is in the second quadrant is.


1.

A.30
B.60
C.150
D. 240

2.

A.30
B.60
C.150
D.240

Answer 1

1. 30

2. 150

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 = (1)/(3)`

Take square root on both sides

`u = +-(1)/(√(3) )`

We replace tan(x) for 'u'

`tan(x) = +-(1)/(√(3) )`

x = 30 because
`tan(30) =+(1)/(√(3) )` in first quadrant

x = 30 (tan is positive in first quadrant)

`tan(x) =-(1)/(√(3) )`

x = 150 because
`tan(150) =-(1)/(√(3) )` in second quadrant

tan is negative in second quadrant