Pre-Calc help please??

Question

1. The domain of validity for the identity sinθ=tanθ cosθ is the set of all real numbers. True or False. And why?


2. How many numbers between 0 and 2π solve the equation 3cos^2x+cosx=2?
A. none
B. 1
C. 2
D. 3
E. 4

Answer 1

It is false as tan x is not defined for x=kpi/2 while sin(theta9 is defined for all theta
3cos^2x+cosx-2=0 If you call cosx=z
3z^2+z-2=0
z=((-1+-5)/6
z=-1 and z= 2/3
cos x= -1 so x= pi
cos x= 2/3 so x=0.7859 and x = 5.4973 radians
so there are three solutions between 0 and 2 pi