An equation is given Enter your answers as a commaseparated

An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.)

1 2 sin() = cos(2)

(a) Find all solutions of the equation.
=    

(b) Find the solutions in the interval [0, 2).
=   

Solution

1-2sin theta= cos 2 theta

1-2sin theta= 1-2sin²theta

2sin²theta - 2sin theta=0

2sin theta(sin theta -1)=0

sin theta=0, sin theta=1

theta= pi, pi/2