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$I f f, g, h, ϕ a r e f u n c t i o n s f r o m R \to R$
List - I
I. $f (x) = \sin^{3} x + 2 \sin x + \sin 3 x$ a) even function
II. $g (x) = \cos 3 x + \sin^{4} x + 3 \cos x$ b) odd function
III. $h (x) = \sin 3 x + \cos 2 x + \sin^{2} x$ c)both even and odd function
IV. $ϕ (x) = \frac{\tan [x] π}{1 + \sin [x] π}$ d)neither even nor odd function

I. $f (x) = \sin^{3} x + 2 \sin x + \sin 3 x$	a) even function
IV. $ϕ (x) = \frac{\tan [x] π}{1 + \sin [x] π}$	d)neither even nor odd function

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I-a; II-b; III-d; IV-c

I-b; II-a; III-d; IV-c

I-b; II-a; III-c; IV-d

I-a; II-b; III-c; IV-d

answer is D.

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Detailed Solution

$f (- x) = - f (x) \Rightarrow f (x)$ is odd

$g (- x) = g (x) \Rightarrow g (x)$ is even

$h (x) = \sin 3 x + \cos 2 x + \sin^{2} x$

$h (- x) = - \sin 3 x + \cos 2 x + \sin^{2} x$

$∴ h (x)$ is neither even nor odd

$ϕ (x) = 0$ is both even and odd

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