I need some help with the domains of trig equations.

I have solved all the equations i believe with the right answers, , you can recheck it if you feel comfortable.

a. cos2x+cosx=0

ANS:

2cosx^2+cosx-1

(2cosx-1)(cosx+1)

x = 1/2 and x = -1

x = pi/3 ,5pi/3 and -pi

are these the right answers in the domain x is an element [-pi,pi) - i believe the [ means equal to and the bracket means doesnt equal

b. 2cosx^2+3sinx=0

2(1-sinx^2)+3sinx=0

2-2sinx^2+3sinx

2sinx^2-3sinx-2

(2sinx-1)(sinx+2)

sinx=1/2 sinx=-2 - cancels since -2 isnt on the unit circle

x = 30 and 150 degrees -- in the domain [0,360]

c. cos2x-cosx^2=0

2cosx^2-1-cosx^2

cosx^2-1

(cosx+1)(cosx-1)

cosx=-1 cosx= 1

x = pi and 0 ---- in the domain [-pi,pi]

i just have a hard time with these domains for the trig equations, can someone please check over my answers to see if it fits the domains, or if i have to get rid of some answers or add some answers.

Thank you in advance

proving identities.

cosx-sinx/cosx = 1-tanx

can someone prove this identity for me?