Question

If $f(x)=x^3-x$ and $\varphi (x)=sin2x,$ then find the value of $8f\varphi \frac{\pi }{12}$.

Answer 1

Answer: 3

$f(x)=x^3-x,\varphi (x)=sin2x$
$\Rightarrow f\varphi \frac{\pi }{12}=f\sin \frac{2\pi }{12}$ $=f\sin \frac{\pi }{6}=f\frac{1}{2}$ $={\left(\frac{1}{2}\right)}^3-\frac{1}{2}$
$=\frac{1-4}{8}=-\frac{3}{8}$
$=-0.375$
$\Rightarrow 8f\varphi \frac{\pi }{12}=3$