MCQ
Statement $A\left(\right.$ Assertion) : If $\sin \theta=\frac{1}{2}$ and $\theta$ is acute angle, then $\left(3 \cos \theta-4 \cos ^3 \theta\right)$ is equal to 0.Statement R (Reason) : As $\sin \theta=\frac{1}{2}$ and $\theta$ is acute, so $\theta$ must be $60^{\circ}$.
  • A
    Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
  • B
    Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
  • Assertion $(A)$ is true but reason $(R)$ is false.
  • D
    Assertion (A) is false but reason $(R)$ is true.

Answer

Correct option: C.
Assertion $(A)$ is true but reason $(R)$ is false.
(c) : We have, $\sin \theta=\frac{1}{2}$
$\Rightarrow \theta=30^{\circ} \quad\left[\because \sin 30^{\circ}=\frac{1}{2}\right]$
$\therefore 3 \cos \theta-4 \cos ^3 \theta=3 \cos 30^{\circ}-4 \cos ^3 3 \sigma^{\circ}$
$
=\frac{3 \sqrt{3}}{2}-4\left(\frac{\sqrt{3}}{2}\right)^3=\frac{3 \sqrt{3}}{2}-\frac{3 \sqrt{3}}{2}=0
$
$\therefore$ Asoertion is true bet Reason is false.

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