Question

sinα=-4/5,α∈(π,3π/2),cosβ=-12/13,β∈(π/2,π).

sin(α+β) 的值 cos^2α的值
cos2α的值

Answer 1

sinα=-4/5
=>cosα=-3/5
cosβ=-12/13
=>sinβ=5/13

sin(α+β)
=sinαcosβ+cosαsinβ
=(-4/5)(-12/13)+(-3/5)(5/13)
=33/65

cos2α
=（cosα）^2-（sinα）^2
=（-3/5）^2-（-4/5）^2
=-7/25

Answer 2

sinα=-4/5
=>cosα=-3/5
cosβ=-12/13
=>sinβ=5/13

sin(α+β)
=sinαcosβ+cosαsinβ
=(-4/5)(-12/13)+(-3/5)(5/13)
=33/65

(cosα)^2 = 2(cosα)^2-1 = 2(9/25)-1 = -7/25