Find minimum value of 2cos x + 2cos y

To find the minimum value of the expression 2cos(x) + 2cos(y), we need to determine the range of both cos(x) and cos(y) individually and then combine them to find the minimum value.

The function cos(x) has a range between -1 and 1, meaning that it can take any value within this interval. Similarly, cos(y) also has a range between -1 and 1.

To find the minimum value of the given expression, we want both cos(x) and cos(y) to be as small as possible. The smallest value for cos(x) is -1, and the smallest value for cos(y) is also -1.

So, the minimum value of 2cos(x) + 2cos(y) occurs when both cos(x) and cos(y) are at their minimum values of -1.

Substituting -1 into the expression, we get:

2*(-1) + 2*(-1) = -2 - 2 = -4

Therefore, the minimum value of 2cos(x) + 2cos(y) is -4 when cos(x) = cos(y) = -1.