Вычислите: (sin(pi/8)+sin(3pi/8)) (cos(3pi/8)-cos(pi/8))

Question

Вычислите: (sin(pi/8)+sin(3pi/8)) (cos(3pi/8)-cos(pi/8))

Answer 1

(sin(π/8)+sin(3π/8))*(cos(3π/8)-cos(π/8))=

sinα+sinβ=2*sin(α+β)/2*cos(α-β)/2;

cosα-cosβ=(-2)*sin(α+β)/2*sin(α-β)/2;

 

(sin(π/8)+sin(3π/8))*(cos(3π/8)-cos(π/8))=(2sin(π/4)*cos(π/8))*(-2sin(π/4)*sin(π/8))=

-2cos(π/8)*sin(π/8)=-sin(π/4)=-√2/2.