Question

If $\sin B=\frac{1}{2}$ what is the value of $3\cos B-4{\cos }^{3}B?$

• A. 1
• B. 4
• C. 2
• D. 0

Answer 1

Answer: (D)

0

$SinB=\frac{1}{2}$

$\because sin{30}^{\circ }=\frac{1}{2}$

$\therefore B={30}^{\circ }$

the put the value of B in $3cosB-4co{s}^{3}B$

$\Rightarrow 3cos{30}^{\circ }-4co{s}^3{30}^{\circ }$

$\because cos{30}^{\circ }=\frac{\sqrt{3}}{2}$ then

$\Rightarrow 3\times \frac{\sqrt{3}}{2}-4\times (\frac{\sqrt{3}}{2}{)}^3$

$\Rightarrow \frac{3\sqrt{3}}{2}-\frac{4\times 3\sqrt{3}}{8}$

$\Rightarrow \frac{3\sqrt{3}}{2}-\frac{3\sqrt{3}}{2}=0$