Evaluate the exact value of the trigonometric expression: (1/root2)*cot 30° + (1/root3)*cosec 60° Give the answer in simplest exact form (no decimals).

Introduction / Context:
This question checks standard trigonometric values at special angles and algebraic simplification involving surds (square roots). You must substitute exact values for cot 30° and cosec 60° and then add carefully as fractions.

Given Data / Assumptions:

• Expression: (1/root2)*cot 30° + (1/root3)*cosec 60°
• Use exact special-angle values (no rounding).

Concept / Approach:
Recall: cot 30° = root3 sin 60° = root3/2, so cosec 60° = 1/sin 60° = 2/root3 Then substitute and simplify each term separately before adding with a common denominator.

Step-by-Step Solution:

Verification / Alternative check:
You can confirm by approximate checking: root6 is about 2.449, so (3*2.449 + 4)/6 is about (7.347 + 4)/6 = 11.347/6 ≈ 1.891, matching root6/2 (≈1.225) plus 2/3 (≈0.667).

Why Other Options Are Wrong:

Common Pitfalls:
Mixing up cosec 60° with sec 60°, or forgetting that (1/root3)*(2/root3) equals 2/3, not 2/root3.

Final Answer:
(3*root6 + 4)/6