1 已知 cos(π/4-α)=3/5,sin(5π/4+β)=-12/13,α∈(π/4,3π/4),β∈(0,π/4

1。sin(α+β)=-sin[(5π/4+β)-(π/4-α)]=-sin(5π/4+β)*cos(π/4-α)+cos(5π/4+β)*sin(π/4-α)由：α∈(π/4,3π/4),β∈(0,π/4）得 （π/4-α）∈(-π/2,0),(5π/4+β)∈(5π/4,3π/2)从而 sin(π/4-α)=-4/5,cos(5π/4+β)=-5/13 代入第一式 =-(-12/13)*3/5+(-5/13)*(-4/5)=56/652。α,β都是锐角,tanβ=sinβ/cosβ=(根号10/10)/(3根号10/10)=1/3,得 tan(α+2β)=tan[(α+β)+β]tan[(α+β)+β]=(tan(α+β)+tanβ)/(1-tan(α+β)*tanβ)又 tan(α+β)=（tanα+tanβ)/(1-tanα*tanβ)=1/2 代入上式 得 tan(α+2β)=tan[(α+β)+β]=13。y=(sinx+cosx)^2+2cos^2x=cos^2x+sin^2x+2sinx*cosx+2cos^2x也就等于 =1+2sinx*cosx+2cos^2x=1+2sinx*cosx+cos(2x)+1=1+sin(2x)+cos(2x)+1=2+根号2sin(2x+π/4)sin函数 减区间为 (2kπ+π/2)