SOLUTION: i'm so confused about this question. i don't know what formula will i going to use and where to start. please help me. 9 cos (2theta)= -9 cos theta please show me step by ste

First divide both sides by 9. You will get an EQUIVALENT equation


    cos(2theta) = - cos(theta)


Next, use the standard basic trigonometry formula


    cos(2theta) = 2*cos^2(theta) - 1.


Then equation (1) takes the form


    cos^2(theta) = -cos(theta),   or


    cos^2(theta) + cos(theta) = 0.


Factor it


    cos(theta)*(cos(theta) + 1) = 0.


Hence, EITHER  cos(theta) = 0,  giving solutions   =  + ,  k = 0, +-1, +-2, . . . 


       OR  cos(theta) = -1,  giving solutions   = ,  k = 0, +-1, +-2, . . .