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  4. If f(.x.)=x3-x and φ(.x.)=sin2x, then find the value of 8 f φ (π/12).

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

NTA AbhyasNTA Abhyas 2022

Solution:

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