Question

If $\sin \theta =\frac{1}{2}$, then find $3\cos \theta -4{\cos }^3\theta$

Answer 1

$\sin \theta =\frac{1}{2}$

$\Rightarrow \theta =\frac{\pi }{6}$

Now,

$3\cos \theta -4{\cos }^3\theta =-\cos 3\theta$

$=-\cos \left(\frac{\pi }{2}\right)=0$