1.设cos(α+π/4)=2/3,求sin2α的值；2.已知sinθ=3/5,θ∈(π/2,π),求cos(2θ-2π/3)的值_数学解答

1.设cos(α+π/4)=2/3,求sin2α的值；2.已知sinθ=3/5,θ∈(π/2,π),求cos(2θ-2π/3)的值.

人气：308 ℃　时间：2020-05-13 13:09:32

解答

1sin2α=cos(α-π/2)=-cos(α+π/2)=-[2cos^2(α+π/4)-1]=1-2×(2/3)^2=1/92cosθ=-√(1-sin^2θ)=-4/5;cos(2θ-2π/3)=2cos^2(θ-π/3)-1=2[cosθ·cos(π/3)+sinθ·sin(π/3)]-1=2[(-4/5)(1/2)+(3/5)(√3/2)]-1...