Answer:
Option B
Step-by-step explanation:
We have tan^2( x ) + sec( x ) = 1.
First subtract 1 from either side, applying the identity tan^2( x ) = - 1 + sec^2( x ) = - 2 + sec( x ) + sec^2( x ) = 0
One key method that you should use to solve like problems, is to substitute a rather large value with a variable, such as say a. Let sec( x ) = a,
- 2 + a + a^2 = 0,
By the zero product property, a = 1, a = - 2. Substitute this value of a back into sec( x ) -
sec( x ) = 1, sec( x ) = - 2
From this we can create inequality( s ) as follows -
sec( x ) = 1, 0 ≤ x ≤ 2π, x = 0 and x = 2π
sec( x ) = - 2, 0 ≤ x ≤ 2π, x = 2π / 3 and x = 4π / 3
As you can see, x is the following solutions -
0, 2π, 2π / 3, 4π / 3
Eliminate 2π, and it should be that your solution is option B
