【若tan(α-π/4)=1/2,且α属于(0,π/2),则sinα+cosα=】

网友回答

tan(a-π/4)=(tana-1)/(1+tana)=1/2
1+tana=2tana-2
tana=3
因为0======以下答案可供参考======
供参考答案1:
tana=3
所以sin=0.3 cos=0.1 s+c=0.4供参考答案2:
tan(α-π/4)=(tanα-1)/(tanα+1)=1/2
tanα = 3
(cosα)^2 = 1/10
则sinα + cosα = cosα (1+tanα )=4/(10)^(1/2)
供参考答案3:
tan(α-π/4)=1/2
(tanα-tanπ/4)/((1+tanαtanπ/4)=1/2
(tanα-1)/((1+tanα)=1/2
2tanα-2=1+tanα
tanα=3
sin2α=2tanα/[1+(tanα)²]=2*3/[1+9]=6/10=3/5
(sinα+cosα)²=1+2sinαcosα=1+sin2α=1+3/5=8/5
sinα>0,cosα>0sinα+cosα=2√10/5