Evaluate tan 75\(^o\); leaving the answer in surd form (radicals)

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 + \(\sqrt{3}\)