Solve the equation 2Cos2x Sin x 1 for all x such that 0 le

Solve the equation 2Cos^2x + Sin x = 1 for all x such that 0 lessthanorequalto x lessthanorequalto 2pi. Find all angles of oblique triangle ABC if a = 12\', b = 5\', and c = 16\'. Round solutions to nearest degree.

Solution

2cos²x + sinx=1

2(1-sin²x) + sinx=1

2sin²x -sinx -1=0

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

2sinx +1=0    ,     sinx-1=0

sin x=-1/2      ,        sin x=1

x=sin^-1(-1/2)   ,          x=sin^-11

x= 7pi/6, 11pi/6, pi/2