Question

$\text{If}sin\theta =\frac{1}{2}$
and $\theta$ is acute,
$\text{then find the value of}(3cos\theta -4co{s}^3\theta ).$

• A. $0$
• B. $\frac{1}{2}$
• C. $\frac{1}{6}$
• D. $-1$

Answer 1

The correct option is A $0$

Given,
$sin\theta =\frac{1}{2}\Rightarrow \theta ={30}^{\circ }$
Now,
$3cos\theta -4co{s}^3\theta =3cos{30}^{\circ }-4co{s}^3{30}^{\circ }=3\times \frac{\sqrt{3}}{2}-4\times (\frac{\sqrt{3}}{2}{)}^3=\frac{3\sqrt{3}}{2}-\frac{4\times 3\sqrt{3}}{8}=\frac{3\sqrt{3}}{2}-\frac{3\sqrt{3}}{2}=0$