Question

Cos(2П/3-a)-cos(a+П/3)

Answer 1

Cos2П/3соsa+sin2П/3sina-cosacosП/3+sinasinП/3=-1/2соsa+koren3/2sina-1/2cosa+koren3/2sina=-cosa+koren3sina

Answer 2

To simplify the expression cos(2π/3 - a) - cos(a + π/3), you can use trigonometric identities.

First, let's use the difference of angles identity for cosine:

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

In this case, let A = 2π/3 and B = a, so we have:

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

Now, let's use the values of cos(2π/3) and sin(2π/3).

cos(2π/3) = -1/2 sin(2π/3) = √3/2

So, our expression becomes:

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

Next, use the sum of angles identity for cosine:

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

In this case, A = a and B = π/3, so we have:

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

Now, let's use the values of cos(π/3) and sin(π/3).

cos(π/3) = 1/2 sin(π/3) = √3/2

So, our expression becomes:

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

Now, simplify the expression:

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

Now, you can see that (-1/2)cos(a) and (-1/2)cos(a) cancel each other out, and (√3/2)sin(a) and - (√3/2)sin(a) also cancel each other out. So, the expression simplifies to:

0

So, the simplified expression is 0.