Question

If $f\left(x\right)=\sin x$ and $g\left(x\right)=\cos x$ then $D\ast (f\circ g)$ is equal to

• A. $-\sin 2\left(\cos x\right)\sin x$
• B. $-\sin \left(\cos x\right)\sin x$
• C. $-{\sin }^2\left(\cos x\right)\sin x$
• D. $-\sin \left(\cos x\right){\sin }^{2}x$

Answer 1

The correct option is A $-\sin 2\left(\cos x\right)\sin x$

Given, $f\left(x\right)=\sin x,g\left(x\right)=\cos x$
$\Rightarrow fog=\sin \left(\cos x\right)$
$\therefore D\ast \left(fog\right)=2\sin \left(cosx\right).\cos \left(\cos x\right)(-\sin x)$

$=-\sin \left(2\cos x\right).\sin x$