AP EAMCET · Maths · Functions
The function \(f(x)=\sin x-\cos x\) is ........
- A Odd function
- B Even function
- C Neither even nor odd function
- D \(f(x)\) is not a function
Answer & Solution
Correct Answer
(C) Neither even nor odd function
Step-by-step Solution
Detailed explanation
\[ \text { } \begin{aligned} f(x) & =\sin x-\cos x \\ f(-x) & =\sin (-x)-\cos (-x) \\ f(-x) & =-\sin x-\cos x \\ f(-x) & =-(\sin x+\cos x) \\ f(-x) & \neq f(x) \end{aligned} \] \(\therefore f(x)\) is neither even nor odd function. Hence, option (3) is correct.
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