Determine the nature of the following functions for even and odd
$f (x) = sin x + cos x$

Open in App

Solution

Given, $f (x) = sin x + cos x$
$f (- x) = sin (- x) + cos (- x) = - sin x + cos x$
$∴ f (x) \neq f (- x)$ Hence nither even nor odd.

Suggest Corrections

Similar questions

f (x) = x^{2} - [x]

How many of the following functions are even [sin x is odd and cosx is even]

(a) f(x) = $x^{2} | x |$ (b) f(x) = $e^{x} + e^{- x}$

(e) f(x) = log(x + $\sqrt{x^{2} + 1}$ (f) $a^{x} - a^{- x}$

(g) f(x) = $sin x + cos x$ (h) $sin x \times (e^{x} - e^{- x})$

How many of the following functions are even [sin x is odd and cosx is even]

(a) f(x) = $x^{2} | x |$ (b) f(x) = $e^{x} + e^{- x}$

(e) f(x) = log(x + $\sqrt{x^{2} + 1}$ (f) $a^{x} - a^{- x}$

(g) f(x) = $sin x + cos x$ (h) $sin x \times (e^{x} - e^{- x})$

f (x) = sin x - cos x

Join BYJU'S Learning Program