Use a counter example to show that cos(x+y)= cosx +cosy is not an identity
See:
http://www.jiskha.com/display.cgi?id=1259078808
To show that the equation cos(x + y) = cosx + cosy is not an identity, we need to find a pair of values for x and y that make the equation false.
Let's consider x = π/4 and y = π/4. Plugging these values into the equation, we have:
cos(π/4 + π/4) = cos(π/2) = 0
cos(π/4) + cos(π/4) = √2/2 + √2/2 = √2
Since 0 is not equal to √2, we can conclude that cos(x + y) = cosx + cosy is not true for all values of x and y.
To show that the equation cos(x+y) = cos(x) + cos(y) is not an identity, we can provide a counterexample where the equation does not hold true for all possible values of x and y.
Let's consider x = 0 and y = π/2.
Using the given equation, we have:
cos(0 + π/2) = cos(0) + cos(π/2)
cos(π/2) = 1 + 0
0 = 1
However, we know that cos(π/2) = 0, not 1. Therefore, the equation cos(x+y) = cos(x) + cos(y) fails for x = 0 and y = π/2.
By providing this counterexample, we have shown that cos(x+y) = cos(x) + cos(y) is not an identity, as it does not hold true for all possible values of x and y.