Question

设向量a=(cos(α+β),sin(α+β)),向量b=(cos(α-β),sin(α-β)),且向量a+向量b=(4/5,3/5)(1)求tanα

(2)求(2cos²α/2-3sinα-1)/√2sin(α+π/4)
哪位好心人帮帮忙，在线等，要有具体步骤哦，先谢谢啦

Answer 1

cos(α+β)+cos(α-β)=4/5
cosαcosβ-sinαsinβ+cosαcosβ+sinαsinβ=4/5
cosαcosβ=2/5
cosα=2/5cosβ
sin(α+β)+sin(α-β)=3/5
sinαcosβ=3/10
sinα=3/10cosβ

tanα=sinα/cosα=3/4

(2cos²α/2-3sinα-1)/√2sin(α+π/4)
=(1+cosα-3sinα-1)/(sinα-cosα)
=(cosα-3sinα)/(sinα-cosα)
sinα=cosαtanα
sinα=3(cosα)/4

=(cosα-3*3(cosα)/4)/(3(cosα)/4
-cosα)
=5

(2cos²α/2-3sinα-1)/√2sin(α+π/4)
=5