Given trigonometric equation sin 4x cos 4x sinx cosx solve the equation and find the value of lsquo ...........

Mathematics (NDA) Trigonometry

Given trigonometric equation {sin ⁴x + cos ⁴x = sinx . cosx} ,solve the equation and find the value of ‘x’?

X=nπ +π/4

X=nπ +π/6

X=nπ +π/5

X=nπ +π/3

sin ⁴x + cos ⁴x = sinx cosx

(1-cos2x /2)²+(1+cos2x /2 )² =sinx cosx

(1-cos2x )²+(1+cos2x )² =4sinx cosx

2(1+cos ²2x )=2sin2x

(1+1 –sin² 2x) = sin2x

sin² 2x + sin2x =2

sin2x =1 or sin2x =-2

2x =2nπ+π/2

X=nπ +π/4

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