Find all exact solutions on the interval [0, 2π). (Enter your answers as a comma-separated list.) cos(2t) = sin(t)

Answer 1

Use the identity cos (2x) = 1-sin^2(x)

1-2sin^(x) = sin(x)

2sin^2(x) + sin(x) -1 =0 this will factor to

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

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

2sin(x)=1 sin(x0 = -1

sin x= 1/2

x= p1/6, 5pi/6 x=3pi/2