The function $f(x)=\sin x-\cos x$ is ........

The function $f(x)=\sin x-\cos x$ is ........
  1. Odd function
  2. Even function
  3. Neither even nor odd function
  4. $f(x)$ is not a function

Solution

$ \text { } \begin{aligned} f(x) & =\sin x-\cos x \\ f(-x) & =\sin (-x)-\cos (-x) \\ f(-x) & =-\sin x-\cos x \\ f(-x) & =-(\sin x+\cos x) \\ f(-x) & \neq f(x) \end{aligned} $ $\therefore f(x)$ is neither even nor odd function. Hence, option (3) is correct

Asked in: AP EAMCET 2020 (22 Sep Shift 2)

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