If $cos θ = \frac{7}{3\sqrt{6}}$ and θ is an acute angle, then the value of $27 sin^2 θ - \frac{3}{2}$ is :
Answer & explanation
Correct answer: option 3
$cos θ = \frac{7}{3\sqrt{6}}$
cos²θ = \(\frac{49}{54}\)
Now,
27sin²θ - \(\frac{3}{2}\)
= 27 ( 1 - cos²θ ) - \(\frac{3}{2}\)
= 27 ( 1 - \(\frac{49}{54}\) ) - \(\frac{3}{2}\)
= 27 ( \(\frac{5}{54}\) ) - \(\frac{3}{2}\)
= \(\frac{5}{2}\) - \(\frac{3}{2}\)
= 1