Please help me to solve x , 0 <= x <= 360, where
3 tan x - 2 + 3 sec x = 2 cosec x
Thank you
<-- Clear the fractions
We want to get this equation in terms of a single trig function. We can do that by employing , so we need to do the following:
<-- Square both sides
Now . (If we hadn't squared the equation we'd've had to choose which quadrant x is in.)
Now let
This is ugly. BUT, if we use the rational root theorem we know that all the possible rational roots are at . It turns out that is a rational zero. So by division we get that
We may apply the rational root theorem again to find that is again a zero of the cubic polynomial, or you may note that we may factor the cubic polynomial by grouping:
So:
So we have that
and
The solution generates
The other two are not so nice. We obtain:
which has only the approximate solutions:
and
which has only the approximate solutions:
-Dan
PS Whoops! I almost forgot. We need to check each of these solutions in the original equation to be sure that they ARE actually solutions. I get that only the solutions work.
Graphically solving the problem makes it appear that is also a solution. However this x value can't be a solution because is undefined.
-Dan