Question

If f(x)=sinx + cosx show that f(x+pi)=-f(x)

Answer 1

$f(x) = cosx + sinx \\ f(x + \pi) = cos(\pi + x) + sin(\pi + x) = - cosx - sinx \\ = - (cosx + sinx) \\ = - f(x) \\ since \: cos(\pi + x) = - cosx \: \: and \: \: sin(\pi + x) = - sinx$
hope it helps