Question : If $\sin \theta=\frac{1}{2}$, then the value of $\left(3 \cos \theta-4 \cos ^3 \theta\right)$ is:
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: – 1
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Correct Answer: 0
Solution :
Given, $\sin \theta=\frac{1}{2}$
⇒ $\theta = 30^\circ$
Now, $\left(3 \cos \theta-4 \cos ^3 \theta\right)=-\cos 3\theta$
⇒ $\left(3 \cos \theta-4 \cos ^3 \theta\right)=-\cos 90^\circ$
⇒ $\left(3 \cos \theta-4 \cos ^3 \theta\right)=0$
Hence, the correct answer is 0.
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