Sin^6(x)+cos^6(x)=(5/4)sin^2(2x)

Question

Sin^6(x)+cos^6(x)=(5/4)sin^2(2x)

Answer 1

sin^6(x)+cos^6(x)=(5/4)sin^2(2x)
sin^6(x)+cos^6(x) = 5 sin^2(x)*cos^2(x)
(sin^2(x)+cos^2(x))(sin^4(x)+cos^4(x)-sin^2(x)cos^2(x)) = 5/4sin^2(2x)
1/8(3cos(4x)+5) = -5/8(cos(4x)-1)
cos(4x) = 0
x = πn-(7π)/8
x = πn-(5π)/8
x = πn-(3π)/8 
x = πn-π/8
n ∈ Z