Cos (α — β) , если cos α = — 2/5, sin β = — 5/13; 90° < α < 180°, 180° < β < 270°;

Question

Cos (α — β) , если cos α = — 2/5, sin β = — 5/13; 90° < α < 180°, 180° < β < 270°;

Answer 1

cos (α — β)=(cosα)(cosβ)+(sinα)*(sin β)

sinα=√(1-cos²α)=√(1-4/25)=√21/5

cosβ=-√(1-sin² β)=-√(1-25/169)=-12/13

cos (α — β)=( — 2/5)(-12/13)+(— 5/13)*(√21/5)=(24-5√21)/65