What is (\frac{\sqrt{3}p}{4} - \frac{q}{4}) equal to?
For the following two (02) items: Let p = \csc 20^\circ and q = \csc 70^\circ.
- A. -1
- B. 0
- C. 1 ✓
- D. 2
Correct Answer: C. 1
Explanation
We have p = \frac{1}{\sin 20^\circ} and q = \frac{1}{\cos 20^\circ}. The expression is \frac{\sqrt{3}\cos 20^\circ - \sin 20^\circ}{4\sin 20^\circ\cos 20^\circ} = \frac{2(\sin 60^\circ\cos 20^\circ - \cos 60^\circ\sin 20^\circ)}{2\sin 40^\circ} = \frac{2\sin 40^\circ}{2\sin 40^\circ} = 1.