If Sin \(\theta\) = \(\frac{\sqrt{3}}{2}\) and \(\theta\) is less than 90º, calculate \(\frac{tan(90 – \theta)}{cos^2\theta}\)

Explanation

If Sin \(\theta\) = \(\frac{\sqrt{3}}{2}\), then \(\theta\) = 60º

∴ \(\frac{tan(90 - \theta)}{cos^2\theta}\) = \(\frac{tan(90 - 60)}{cos^2 60}\) = \(\frac{tan30}{cos^2 60}\)

= \(\frac{1}{\sqrt3} \times (\frac{2}{1})^2 = \frac{4}{\sqrt{3}}\)