If Sin \(\theta\) = \(\frac{\sqrt{3}}{2}\) and \(\theta\) is less than 90º, calculate \(\frac{tan(90 - \theta)}{cos^2\theta}\)
A
\(\frac{1}{2}\)
B
\(\frac{4}{\sqrt{3}}\)
C
\(\sqrt{3}\)
D
4\(\sqrt{3}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
If Sin \(\theta\) = \(\frac{\sqrt{3}}{2}\), then \(\theta\) = 60º
∴ \(\frac{tan(90 - \theta)}{cos^2\theta}\) = \(\frac{tan(90 - 60)}{cos^2 60}\) = \(\frac{tan30}{cos^2 60}\)
= \(\frac{1}{\sqrt3} \times (\frac{2}{1})^2 = \frac{4}{\sqrt{3}}\)
Source: Myschool Past Questions Archive (Record #32751)