If the equation sin6x+cos6x=λ2 has a solution, then λ belongs to
f(x)=λ2=sin6x+cos6x
=(sin2x+cos2x)3−3sin2xcos2x(sin2x+cos2x)
=1−3sin2xcos2x[∴(a3+b3)=(a+b)3−3ab(a+b)]
f(x)=λ2=1−34(sin2x)2
∴ range of f(x)ϵ[1−34(1),1−34(0)]
λ2ϵ[14,1]
⇒λϵ[12,1]∪[−1,−12]