Please find all solutions in radians 2sin24xcos4x1Solution2

Please find all solutions in radians. 2sin^2(4x)-cos(4x)=1

2 sin^2(4x) - cos(4x) = 1

subtract 1 from both sides

2 sin^2 (4x) - cos (4x) -1 =0

sin^2(4x) = 1- cos^2(4x)

plugging the value we get

1-cos (4x)-2cos^2(4x) =0

plug cos (4x) = y

1 - y - 2y^2 =0

on solving the quadratic we get

y = -1

y = 1/2

cos (4x) = -1

cos (4x) = 1/2

x = ( pi + 2pi*n)/4

x = (6 pi*n + pi ) /12 , (6 pi*n + 5pi ) /12