To simplify the expression 1 – cos x1 cos x, we can use the trigonometric identity that relates the product of cosine functions to a sum of sines.
We start with the product cos x1 cos x, which can be rewritten using the identity:
cos A cos B = (1/2)(cos(A + B) + cos(A – B))
Applying this identity, we get:
cos x1 cos x = (1/2)(cos(x1 + x) + cos(x1 – x))
Now, substituting this back into our original expression:
1 – cos x1 cos x = 1 – (1/2)(cos(x1 + x) + cos(x1 – x))
Next, we simplify it further:
1 – (1/2)(cos(x1 + x) + cos(x1 – x)) = 1 – (1/2)cos(x1 + x) – (1/2)cos(x1 – x)
Thus, the simplified form of the expression is:
1 – (1/2)cos(x1 + x) – (1/2)cos(x1 – x)
This is the final result.