Question

The value of $4{\cos }^3{40}^{\circ }-3\sin {50}^{\circ }$ is

• A. $-\frac{\sqrt{3}}{2}$
• B. $\frac{1}{\sqrt{2}}$
• C. $\frac{1}{2}$
• D. $-\frac{1}{2}$

Answer 1

The correct option is D $-\frac{1}{2}$

$4{\cos }^3{40}^{\circ }-3\sin {50}^{\circ }=4{\cos }^3{40}^{\circ }-3\cos {40}^{\circ }$

We know that,
$\cos 3x=4{\cos }^{3}x-3\cos x$
Therefore,
$4{\cos }^3{40}^{\circ }-3\cos {40}^{\circ }=\cos {120}^{\circ }$
$=\frac{-1}{2}$