If sin4 2x cos4 2x sin 2x cos 2x then solution of the equation is ........

Mathematics (NDA) Trigonometry

If {sin⁴ 2x + cos⁴ 2x = sin 2x. cos 2x} then solution of the equation is?

x =n π/4 +(-1)ⁿπ/3

x =n π/4 +(-1)ⁿπ/4

x =n π/4 +(-1)ⁿπ/8

x =n π/4 +(-1)ⁿπ/6

sin⁴ 2x + cos⁴ 2x = sin 2x. cos 2x

let sin 2x. cos 2x =y

sin⁴ 2x + cos⁴ 2x=1- 2sin² 2x cos² 2x

1- 2sin² 2x cos² 2x = sin 2x. cos 2x

1-2y² =y

2(y+1)(y- 1/2)=0

Y =1/2

sin 2x. cos 2x =1/2

2 sin 2x. cos 2x =1

Sin4x =1

4x =π/2

X= π/8

x =n π/4 +(-1)ⁿπ/8

Y= -1

sin 2x. cos 2x=-1

2sin 2x. cos 2x =-2

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