Solving for All Values of x in (cos2x)/(sin3x-sinx) = 1

[xtpacygax]

Solve for all values of x:

(cos2x)/(sin3x-sinx) = 1

I found this problem and am having an extremely tough time solving it. I gotten down to a quadratic equation a couple of times, but it wouldn't factor. I am really stumped and really need some help. Thanks in advance.

 

[ZioX]

Solve for all values of x:

(cos2x)/(sin3x-sinx) = 1

I found this problem and am having an extremely tough time solving it. I gotten down to a quadratic equation a couple of times, but it wouldn't factor. I am really stumped and really need some help. Thanks in advance.

Don't you know how to solve all quadratic equations?

 

[xtpacygax]

Yes, I know how to solve quadratic equations, but I would get a negative under the radical and it would be undefined so the equation would not be possible. I think I found an answer and would like if someone could confirm this.

For the final equation I got:

sinx = 1/2

and then I got:

x = (pi)/6 + 2(pi)k
x = 5(pi)/6 + 2(pi)k

(Sorry, I don't know how to make a pi symbol)

 

[HallsofIvy]

You have shown really none of your work so it's impossible to say where you might have gone wrong. Reducing the orginal formula to sin x, I get a cubic equation which has an obvious root of sin x= 1/2 and the remaining quadratic is just 2x²- 1= 0!