Use a counter example to show that cos(x+y)= cosx +cosy is not an identity

Answer 1

Let x=π/4, y=π/4,
cos(x+y)
=cos(π/4+π/4)
=cos(π/2)
=0
cos(x)+cos(y)
=cos(π/4)+cos(π/4)
=√2/2+√2/2
=√2
Since √2 ≠ 0,
cos(x+y) ≠ cosx +cosy