I'm not sure if I am doing these problems right. And for some of them I can`t figure out how they would be factored. I'll e-mail what I have done so far.

Solve each problem for theta(there is no sign on my computer)for 0 is less than or equal to theta which is less less than 360

1. 2cosx-1=0
   cosx=1/2
   Anwser 60,300
   
   
2. tanx-2sinxtanx=0
   tanx(-2sin+1)=0 (factor ?)
   tanx=0 and sin= 1/2 (solve from there?)
   
   
3. 2sinx-cscx=0
   2sinx-1/sinx=0
   3sinx-1=0
   3sinx=1/3(?)
   
   
4. 4cos(2x)+2cosx= -1
   8cosx+2cosx+1=0
   10cosx+1=0
   10cosx= -1/10 (?)
   
   
5. cos(2x-30)=1/2
   cos2x-cos30=1/2
   cos2x-cos30-1/2=0
   i don`t know what to do know
   
   
6. Sinx+cosx=0
   Square both sides?

Here a few hints.

1. 2cosx-1=0
   cosx=1/2
   Anwser 60,300
   
   
2. tanx-2sinxtanx=0
   tanx(-2sin+1)=0 (factor ?)
   tanx=0 and sin= 1/2 (solve from there?)
   
   
3. 2sinx-cscx=0
   2sinx-1/sinx=0
   3sinx-1=0
   3sinx=1/3(?)
   
   Here you have a mistake, you should get 2sin²(x) - 1 = 0
   
4. 4cos(2x)+2cosx= -1
   8cosx+2cosx+1=0
   10cosx+1=0
   10cosx= -1/10 (?)
   
   rather than cos(2x) = 2cos(x) (which is false in general), you should use the identity cos(2x) = cos²(x) - sin²(x) =
   cos²(x) - (1 - cos²(x)) = 2cos²(x) - 1
   
5. cos(2x-30)=1/2
   cos2x-cos30=1/2
   cos2x-cos30-1/2=0
   i don`t know what to do know
   
   In 1) you solved cosy=1/2 Anwser y = 60,300. Therefore for cos(2x-30)=1/2 you get the answer 2x+30 = 60, 300.
   
6. Sinx+cosx=0
   Square both sides?