Question

Cos(альфа+П/3)+cos(П/3-альфа)

Answer 1

Решение во вложении.)

Answer 2

To simplify the expression, let's use the trigonometric identity for the sum of angles:

cos(A + B) = cos(A)cos(B) - sin(A)sin(B)

We can apply this identity to the given expression:

cos(α + π/3) + cos(π/3 - α)

Using the identity, we have:

= cos(α)cos(π/3) - sin(α)sin(π/3) + cos(π/3)cos(α) - sin(π/3)sin(α)

Notice that cos(π/3) = 1/2 and sin(π/3) = √3/2.

= (cos(α)/2 - √3sin(α)/2) + (1/2cos(α) - √3/2sin(α))

Combining like terms, we get:

= 3/2cos(α) - √3/2sin(α)

So, the simplified expression is: 3/2cos(α) - √3/2sin(α)