已知θ属于[0,π/4],sinθ四次方+cosθ四次方=5/8,求θ的大小

Question

如题所述

Answer 1

解：∵θ属于[0,π/4]，则2θ属于[0,π/2]
∴sin(2θ)>0
∵(sinθ)^4+(cosθ)^4=5/8
==>(sinθ)^4+(cosθ)^4+2(sinθcosθ)^2-2(sinθcosθ)^2=5/8
==>((sinθ)^2+(cosθ)^2)^2-2(sinθcosθ)^2=5/8
==>1-2(sinθcosθ)^2=5/8
==>2(sinθcosθ)^2=3/8
==>4(sinθcosθ)^2=3/4
==>(sin(2θ))^2=3/4
==>sin(2θ)=√3/2
==>2θ=π/3
∴θ=π/6。