Express 1 + 2*cos(a) as a product
To express the expression 1 + 2*cos(a) as a product, we need to rewrite it in a form that can be factored.
Recall the trigonometric identity: cos(a) = (e^(ia) + e^(-ia)) / 2.
We can substitute this identity into our expression and simplify:
1 + 2*cos(a) = 1 + 2 * (e^(ia) + e^(-ia)) / 2
= 1 + e^(ia) + e^(-ia)
Now, let's write this expression as a product by factoring:
1 + e^(ia) + e^(-ia) = (1 + e^(ia)) + e^(-ia)
Note that we can recognize this as a sum of two terms being multiplied. We know that the sum of two terms multiplied can be factored using the distributive property.
Using this property, we can express the expression as a product:
(1 + e^(ia)) + e^(-ia) = (e^(ia/2) + e^(-ia/2))(e^(ia/2) + e^(-ia/2))
Therefore, 1 + 2*cos(a) can be expressed as a product: (e^(ia/2) + e^(-ia/2))(e^(ia/2) + e^(-ia/2)).