<u><em>Note: It's not clear if the expressions involving '2x' actually mean squaring the tangent/secant or doubling the angle x. I'm posting the answer assuming the latest approach.</em></u>
Answer:
Step-by-step explanation:
<u>Trigonometric Equations
</u>
It's a type of equations where the variable is the argument of some of the trigonometric functions. It's generally restricted to a given domain, so the solution must be iteratively selected within all the possible answers.
The equation to solve is
Rearranging
Factoring
We come up with two different equations:
Let's take eq 1:
Solving for 2x
There are two sets of possible solutions:
We get two solutions
.
The first solution is out of the range , so it's discarded
.
.
Both solutions are feasible
.
.
Only the first solution lies in the given domain. We won't take negative values of k since it will provide negative values of x and they are not allowed in the solution
Now we solve eq 2:
This leads to the solution
Or equivalently
For k=0, x=0. This solution is valid
For k=1, . This is also valid
For k=2, . This solution is out of range
The whole set of solutions is