What is the answer of the Cos(n+1)a.cos(n-1)+sin(

The expression you provided can be simplified using the cosine and sine addition formulas. Specifically, we can apply the cosine of a sum formula and the sine of a sum formula. Here’s how it works:

Using Trigonometric Identities

The formulas we will use are:

• Cosine Addition Formula: cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
• Sine Addition Formula: sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

Applying the Formulas

In your case, we can rewrite the expression:

cos(n+1)a * cos(n-1)a + sin(n+1)a * sin(n-1)a

This matches the cosine addition formula, where:

A = (n+1)a and B = (n-1)a.

Final Simplification

Thus, we can express the entire equation as:

cos((n+1)a - (n-1)a) = cos(2a).

So, the answer to your expression is:

cos(2a)