is the function f(x)=sinx+cosx, a constant function?

A constant function has the same value for all x.

 

For f(x) = sinx + cosx,

 

f(0)= sin0 +cos0 = 0 +1 = 1

f(pi) = sin(pi) + cos (pi) = 0 + (-1) = -1

 

thus f(0) and f(pi) have diferent values, so f(x) is not a constant function