General Determine 2sinx + cosecx - 3 = 0

[DERRAN]

Homework Statement

determine the general solution of the equation:
2sinx +cosecx -3 = 0

Homework Equations

The Attempt at a Solution

Dont know what to do need help please.

 

[rock.freak667]

What is cosecx equal to?

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

 

[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?

 

[Cyosis]

You should learn to check your answers. Let's 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.

 

[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.

 

[Cyosis]

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

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.

 

[DERRAN]

Thanks for helping

 

[rock.freak667]

Thanks for helping

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