Solve the equation 33 sin theta 6cos 2theta What is the sol

Solve the equation. 3-3 sin theta = 6cos 2theta What is the solution in the interval 0

Solution

given

3-3sin =6cos²

sin²x+cos²x =1 =>cos²x=1-sin²x

3-3sin =6(1-sin² )

3(1-sin) =6(1-sin² )

(1-sin) =2(1-sin² )

1-sin =2-2sin²

2sin² -sin -1=0

2sin² -2sin +sin -1=0

2sin(sin -1)+1(sin -1)=0

(sin -1)(2sin +1)=0

sin -1=0 ,2sin +1=0

sin =1,sin =-1/2

=/2 ,=7/6,11/6

=/2 ,7/6,11/6