Hi, do any of you know how to solve this problem?
Find the only value of x in that satisfies the equation
The answer was , but I don't know how it came to that answer.
Thanks!
First, I'm tempted to change to csc(x) and sec(x), but like many, maybe I'm not all that comfortable with those two functions.
Second, I'm tempted to multiply by sin(x), since sin(x) is never zero in the given interval. Maybe I'm lots more familar with the tangent function.
Third, maybe I'm tempted to get rid of the cosines by the Pythagorean Identity.
Not sure right off. What have you tried?
I'm actually pretty stumped in this problem. This was actually a problem in the national round of one of the math contests here in our country.
The first thing I did was that I ignored the interval I would have as the answer, since and . But then I saw the friggin' interval restriction, and I got lost.
Expressing the equation in terms of cos(x):
.
Let . Equation becomes:
Factorising:
.
This is not the only solution to x. Let us also solve .
Let us finalize our answer:
Can you find the value of x in that satisfies the equation using the general solution from the second factor?