Question

Cos(2/3π-a)+cos(a+π/3)

Answer 1

Ответ:

типа того

Объяснение:

Answer 2

To simplify the expression cos(2/3π - a) + cos(a + π/3), we can use the trigonometric identity:

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

Let's apply this identity to the expression:

cos(2/3π - a) + cos(a + π/3)

Using the identity, we can rewrite the expression as:

cos(2/3π)cos(a) + sin(2/3π)sin(a) + cos(a)cos(π/3) - sin(a)sin(π/3)

Now, we can simplify further:

cos(2/3π) = cos(2π/3) = -1/2 sin(2/3π) = sin(2π/3) = √3/2 cos(π/3) = 1/2 sin(π/3) = √3/2

Substituting these values back into the expression:

(-1/2)cos(a) + (√3/2)sin(a) + (1/2)cos(a) - (√3/2)sin(a)

The terms with cos(a) cancel each other out, and the terms with sin(a) also cancel each other out:

(-1/2 + 1/2)cos(a) + (√3/2 - √3/2)sin(a)

Simplifying further, we get:

0 + 0 = 0

Therefore, the simplified expression is 0.