Question

Чему равно sin 3π/14 cos 4π/14 + cos 3π/14 sin 4π/14

Answer 1

Ответ:

1

Объяснение:

= $sin (\frac{3\pi }{14}+\frac{4\pi }{14} ) =sin \frac{7\pi }{14} =sin\frac{\pi }{2} =1$

Answer 2

Используя формулу для синуса удвоенного угла (sin(2θ) = 2sin(θ)cos(θ)), мы можем упростить данное выражение:

sin(3π/14)cos(4π/14) + cos(3π/14)sin(4π/14)

= sin(3π/14)(2cos²(2π/14) - 1) + 2sin(3π/14)cos(3π/14) = 2sin(3π/14)cos²(2π/14) - sin(3π/14) - 2sin²(3π/14) = 2sin(3π/14)(1 - sin²(2π/14)) - sin(3π/14) - 2(1 - cos²(3π/14)) = 2sin(3π/14)cos²(3π/14) - 2cos²(3π/14) + sin(3π/14) = 2sin(3π/14)(1 - sin²(3π/14)) - 2(1 - sin²(3π/14)) + sin(3π/14) = 2sin(3π/14) - 2sin³(3π/14) - 2 + 2sin²(3π/14) + sin(3π/14) = 3sin(3π/14) - 2sin³(3π/14) - 2

Таким образом, выражение равно 3sin(3π/14) - 2sin³(3π/14) - 2.