If $2\sin θ-1=0$, then find the value of $2\cos^2θ-\sin^3θ$.

$\frac{11}{8}$

sin θ = \(\frac{1}{2}\) = sin 30º

So, θ = 30º

Now, $2\cos^2θ-\sin^3θ$

= $2\cos^230º-\sin^330º$

= 2 × \(\frac{3}{4}\) - \(\frac{1}{8}\) 

=  \(\frac{3}{2}\) - \(\frac{1}{8}\)

= \(\frac{12 - 1}{8}\) 

= \(\frac{11}{8}\)

The correct answer is Option (3) → \(\frac{11}{8}\)