a-maths

sin4x + cos4x = sin2x

(sin2x)2 + (cos2x)2 = sin2x

(sin2x)2 + 2sin2xcos2x + (cos2x)2 = sin2x + 2sin2xcos2x

(sin2x + cos2x)2 = sin2x + 2(sin2xcos2x)2

(1)2 = sin2x + 2[(sin2x)/2]2

(1/2)sin22x + sin2x - 1 = 0

sin22x + 2sin2x - 2 = 0

sin2x = {-2+√[22-4(1)(-2)]}/2 or sin 2x = {-2-√[22-4(1)(-2)]}/2

sin2x = 0.7321 or sin2x = -2.7321(rejected)

2x = 47o or 2x = 180o-47o or 2x = 360o+47o or 2x = 360o+180o-47o

2x = 47o or 2x = 133o or 2x = 407o or 2x = 493o

Hence, x = 23.5o or x = 66.5o or x = 203.5o or x = 246.5o
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