(C) To determine if the function $f(x) = \sin x - \cos x$ is even or odd,we evaluate $f(-x)$:$f(-x) = \sin(-x) - \cos(-x)$Using the trigonometric iden

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(C) To determine if the function $f(x) = \sin x - \cos x$ is even or odd,we evaluate $f(-x)$:$f(-x) = \sin(-x) - \cos(-x)$Using the trigonometric identities $\sin(-x) = -\sin x$ and $\cos(-x) = \cos x$,we get:$f(-x) = -\sin x - \cos x$$f(-x) = -(\sin x + \cos x)$Since $f(-x) \neq f(x)$ and $f(-x) \neq -f(x)$,the function is neither even nor odd.Therefore,option $C$ is correct.

Class 11 Mathematics Relations and Functions Different types of Function

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

AP EAMCET 2020 All AP EAMCET

A
Odd function
B
Even function
C
Neither even nor odd function
D
$f(x)$ is not a function

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