Question

If $2\cos \theta =\sqrt{3}$, evaluate $3\sin \theta -4{\sin }^3\theta$

• A. 3
• B. $\frac{4}{3}$
• C. 1
• D. 2

Answer 1

Answer: (C)

1

$2\cos \theta =\sqrt{3}$

$\Rightarrow \cos \theta =\frac{\sqrt{3}}{2}$

$\Rightarrow \theta =30°$

$\Rightarrow 3\sin \theta -4{\sin }^3\theta =\sin 3\theta [\therefore \sin 3\theta =3\sin 3\theta -4{\sin }^3\theta ]$

$=\sin (3\times 30°)$

$=\sin 90°$

$=1$

Hence, the answer is $1.$