Упростите: sin(3п/5)*sin(7п/5) - cos(7п/5)*cos(3п/5) а) 0 б) -1 в) -cos(п/5) г) 1 д)...

Question

Упростите: sin(3п/5)*sin(7п/5) - cos(7п/5)*cos(3п/5)

а) 0
б) -1
в) -cos(п/5)
г) 1
д) sin(п/5)

Answer 1

Вспомним формулу: cos(α + β) = cosαcosβ - sinαsinβ

- (cos(7π/5)cos(3π/5) - sin(7π/5)sin(3π/5)) = -cos(π/2) = 0

Comments

Спасибо!