Question

Cos2п/7cos5п/7-sin2п/7sin5п/7

Answer 1

Ответ:cos(2pi/7-5pi/7)

Объяснение: cos(a+b)=cosasinb-sinacosb

Answer 2

To simplify the expression cos(2π/7)cos(5π/7) - sin(2π/7)sin(5π/7), we can make use of the trigonometric identity:

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

Let's apply this identity to the given expression:

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

Now, we can simplify further using the periodicity of the cosine function:

cos(-3π/7) = cos(4π/7 - 3π/7) = cos(π/7)

Therefore, the simplified expression is cos(π/7).