Question

If the function f(x) = sin x and g(x) = cos x are one-one in $[0,\frac{\pi }{2}]$, prove that f + g is not one-one in $[0,\frac{\pi }{2}]$.

Answer 1

(f + g) (x) = sin x + cos x

As (f + g) (0) = 1

and (f + g) $\left(\frac{\pi }{2}\right)=1$, f + g is not one-one in $[0,\frac{\pi }{2}]$ .