Given
f (x) = sin x + cos x ... (i)
Now.
Replacing x by - x in (i) we get
f (- x) = sin (- x) + cos ( - x) = - sin x + cos x
[Since cos ( - θ) = cos θ, sin ( - θ) = - sin θ]
Neither f ( - x) = f (x) nor f ( - x) = - f (x)
∴ f (x) is neither an even function nor an odd function
Also, f (x) depends on x . So, f (x) is not a constant function.
Hence, option 'D' is correct