cosα=根号5/5,cosβ=3/5,α,β为第四象限角,则cos(α-β)的值为

1.根号2cosx-根号6sinx利用辅助角公式=2根号2(1/2cosx-2分之根号3sinx0=2根号2sin(π/6-x)2.sin(α-β)cosα-cos(β-α)sinα=3/5sin(α-β)cosa-cos(α-β)sina

/>cos(5π/6+a)=cos[π-(π/6-a)]=-cos(π/6-a)=-√3/3cos²(π/3+a)=cos²[(π/2)-(π/6-a)]=sin²(π/6-a)=1-cos²(π/6

α、β均为锐角,cosα=2√5/5,则sinα=√（1-cos＾2α=√5/5同理sinβ=√10/10则sin(α+β)=sinα.cosβ+cosα.sinβ=3√50/50+2√50/50=√2/2α、β均为锐角,则0

cos(a+π/6)-sina=cosa*cos(π/6)-sina*sin(π/6)-sina=√3/2cosa-3/2sina=3/5*√3cos(a+π/3)=cosa*cos(π/3)-sina*sin(π/3)=1/2cosa-√

|a-b|^2=(a-b)^2=(cosa-cosb)^2+(sina-sinb)^2=2-2cos(a-b),所以,cos(a-b)=17/25.算出sinb,cosb,代入一中结论,用二倍角公式,结合sin^2(a)+cos^2(a)=

因为cos(5π/6+α)=cos[π-(π/6-α)]=-cos(π/6-α),又因为cos(π/6-α)=√3/3,所以：cos(5π/6+α)=-√3/3

sinα-cosα=-根号5/5π

sinα+sinβ=3/5,则(sinα+sinβ)^2=9/25,即(sinα)^2+(sinβ)^2+2sinαsinβ=9/25,同理cosα+cosβ=4/5,则(cosα+cosβ)^2=16/25,即(cosα)^2+(cosβ

cosα+cosβ=3/5sinα+sinβ=4/5两边平方cos²α+2cosαcosβ+cos²β=9/25sin²α+2sinαsinβ+sin²β=16/25相加且sin²x+cos

sinα+sinβ=3/5,则(sinα+sinβ)^2=9/25,即(sinα)^2+(sinβ)^2+2sinαsinβ=9/25,同理cosα+cosβ=4/5,则(cosα+cosβ)^2=16/25,即(cosα)^2+(cosβ

sinα+cosβ=3/5…①cosα+sinβ=4/5...②①²+②²,2+2(sinαcosβ+cosαsinβ)=1∴sin(α+β)=-1/2.①²-②²,cos2α-cos2β+2(cos

记x=cosα,则(cosβ)^2=-5/4x^2+x≥0,解得0≤x≤4/5（而不是0≤x≤1,此步非常关键,大部分同学都会在此处疏漏,导致答案错误）(cosα)^2+(cosβ)^2=-1/4x^2+x=-1/4(x-2)^2+1,由单

∵3π/2

∵α.β都是锐角且cosα=√5/5∴sinα=2√5/5∵sin(α+β)=3/5sinαcosβ+cosαsinβ=√5/5(2cosβ+sinβ)=3/5∴2cosβ+sinβ=3√5/5①∵cosα=√5/5α>π/3√2/2>si

怎么会有负的,都是锐角再问：因为网上有很多都说cos（a+B）是负角

郭敦顒回答：∵cosα=3/5（应是五分之三）,cosβ=（2/5）√5=089442719,∴α=53.130°,β=26.565°,∴sin（α－β）=sin26.565°=0.447213,tan(α+2β)=tan106.260°=

cosα=√10/10,cosβ=√5/5,sinα=3√10/10,sinβ=2√5/5sin(α+β)=sinαcosβ+cosαsinβ=3√2/10+2√2/10=√2/2,cos(α+β)=-√2/2,α+β=3π/4

因αβ均为锐角,所以有：cosα=2√5/5可得：sinα=√5/5cosβ=√10/10　可得：sinβ=3√10/10sin(α-β)=sinαcosβ-cosαsinβ=√5/5x√10/10-2√5/5x3√10/10=-√2/2即

cosα=1/根号10sinα=根号1-cos^2α=根号1-（1/根号10)^2=3/根号10（锐角的正弦必为正数）同理：sinβ=2/根号5所以cos(α+β)=cosαcosβ-sinαsinβ=1/5根号2-6/5根号2=-1/根号

cos(π/12-α)-√3cos(5π/12+α)=2[(1/2)cos(π/12-α)-(√3/2)sin(π/12-α)](∵cos(5π/12+α)=sin[π/2-(5π/12+α)]=sin(π/12-α))=2sin[π/6-