Question

Let $f$ be an odd function defined on the real number such that $f\left(x\right)=3\sin x+4\cos x$

• A. $-3\sin x+4\cos x$
• B. $-3\sin x-4\cos x$
• C. $3\sin x+4\cos x$
• D. $3\sin x-4\cos x$

Answer 1

The correct option is D $3\sin x-4\cos x$

Given, $f\left(x\right)=3\sin x+4\cos x$
When, $x<0$
$\therefore$ $-x>0$
$\therefore f(-x)=3\sin (-x)+4\cos (-x)....\left(i\right)$
But $f\left(x\right)$ is odd function
$\therefore f(-x)=-f\left(x\right)$ when $x<0$
$\Rightarrow f\left(x\right)=-f(-x)=-[3\sin (-x)+4\cos (-x)]=3\sin x-4\cos x$