Q84 / 160 · AP EAMCET 2020 (22 Sep Shift 2) · Mathematics
The function $f(x)=\sin x-\cos x$ is ........
- AOdd function
- BEven function
- Correct answerCNeither even nor odd function
- D$f(x)$ 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.
Hence, the correct answer is option: 'C'.