Question

Without using a calculator or mathematical tables, express in surd form and simplify leaving your answer in the form a + b √c where a, b and c are rational numbers. 
   Cos 30º    
Tan 45 + √3

Answer 1

√ 3/2   
1 +√ 3

√ 3        = √ 3(2-2√ 3)
2 + 2√ 3     (2 + 2 √3 ) (2-2√3)
-2/8√3 + 3/4
= ³/₄ – ¹/₄ √3