Evaluate tan 75\(^o\); leaving the answer in surd form (radicals)
A. \(\sqrt{3 + 2}\)
B. \(\sqrt{3 + 1}\)
C. \(\sqrt{3 - 1}\)
D. \(\sqrt{3 - 2}\)
Correct Answer: D
Explanation
Tan 75\(^o\) = Tan (45\(^o\) + 30\(^o\))
= \(\frac{\tan 45^o + \tan 30^o}{1 - \tan 45^o \tan 30^o}\)
= \(\frac{\sqrt{3} + 1}{\sqrt{3} - 1}\)
RATIONALIZE THE DENOMINATOR
= \(\frac{\sqrt{3} + 1}{\sqrt{3} - 1}\) X \(\frac{\sqrt{3} + 1}{\sqrt{3} +1}\)
= \(\frac{4 + 2\sqrt{3}}{3 - 1}\)
= \(\frac{2(2 + \sqrt{3})}{2}\)
= 2 + \(\sqrt{3}\)
