Foe 0360and using the appropriate identity solve the trigono

Foe 0360°and using the appropriate identity, solve the trigonometric equation 4-5cos=2sin^2

given equation is 4-5cos=2sin^2

but sin^2 + cos^2 =1

so sin^2 = 1 - cos^2

so the equation becomes

4 -5cos = 2[ 1- cos^2]

4 - 5cos = 2 -2cos^2

2cos^2 -5cos +4 -2 =0

2cos^2 -5cos +2=0

2cos^2 -4cos -cos +2=0

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

(cos -2) (2cos -1) =0

this is true when (cos -2) = 0 or (2cos -1) =0

cos = 2 or cos =1/2

this is not possible , so only solution is cos=1/2

so = pi/3(60 degree) , 5pi/3 (300 degree)