Question

求大神帮忙这两道题的答案！跪求！很急，谢谢！

Answer 1

第一道：
∵ π/2 < α < π
∴ cosα < 0
又 cosα² = 1 - sinα² = 1 - 25/169 = 144/169
∴ cosα = 12/13
cos(π/3 + α) = cos(π/3)cosα + sin(π/3)sinα
= 1/2 x 12/13 + √3 x 5/13
= 6/13 + 5√3/13
=(6 + 5√3)/13
第二道：
∵π/2 < α < π
∴ cosα < 0
又 cosα² = 1 - sinα² = 1 - 4/9 = 5/9
∴ cosα = √5/3

∵π < β < 3π/2 ∴sinβ < 0
又 sinβ² = 1 - cosβ² = 1 - 9/25 = 16/25
∴ sinβ = 4/5

cos(α + β) =cosαcosβ - sinαsinβ= -√5 / 5 - 8/15 = - (3√5 + 8)/15