已知tan(θ+π/4)=3,求5sin^2θ-3sinθcosθ+2cos^2θ的值.

来源:学生作业学帮网 编辑:学帮网 时间:2024/06/06 11:11:35

已知tan(θ+π/4)=3,求5sin^2θ-3sinθcosθ+2cos^2θ的值.

tan(θ+π/4)=3
(1+tanθ)/(1-tanθ)=3
tanθ=1/2
5sin^2θ-3sinθcosθ+2cos^2θ=(5sin^2θ-3sinθcosθ+2cos^2θ)/(sin^2θ+cos^2θ)
=(5tan^2θ-3tanθ+2)/(ta^2nθ+1)=(5/4-3/2+2)/(1/4+1)=7/5