# General solution

1. Jun 17, 2009

### DERRAN

1. The problem statement, all variables and given/known data
determine the general solution of the equation:
2sinx +cosecx -3 = 0

2. Relevant equations

3. The attempt at a solution
Dont know what to do need help please.

2. Jun 17, 2009

### rock.freak667

What is cosecx equal to?

When you find that, try multiplying by sinx throughout and see what happens from there.

3. Jun 17, 2009

### DERRAN

Okay I mapped sinx and got:
2sin^{2}x-3sinx+sinx=0
(2sinx-1)(sinx-1)=0
2sinx=1 or sinx=1
sinx=1/2

Is this correct?

4. Jun 17, 2009

### Cyosis

You should learn to check your answers. Lets test it, if sinx=1/2 then the equation becomes:

2*1/4-3*1/2+1/2=-1/2!=0

So no it is not right.

Last edited: Jun 17, 2009
5. Jun 17, 2009

### DERRAN

But x=30 or x=90
then,
substitute in the original equation of 2sinx + cosecx and you get the R.T.P answer of 3.

6. Jun 17, 2009

### Cyosis

I see what happened now. You meant to write 2sin^{2}x-3sinx+1=0 instead of 2sin^{2}x-3sinx+sinx=0. I checked your answer continuing from your first equation, which is wrong. All other steps are correct and your answers satisfy the original equation.

7. Jun 17, 2009

### DERRAN

Thanks for helping

8. Jun 17, 2009

### rock.freak667

Just remember that you were asked to give the general solution and not just solve in a given range.