Question

\(\tan30^\circ\cdot \sin30^\circ\cdot \cot60^\circ\cdot \csc30^\circ=\)

• A. \(1/\sqrt{3}\)
• B. \(\sqrt{3}\)
• C. \(1/(2\sqrt{3})\)
• D. \(1/3\)

Hint:

Know the six trigonometric values at \(30^\circ,45^\circ,60^\circ\); they simplify most exam problems instantly.

Answer 1

The Correct Option is D

Step 1: Insert standard values.
\(\tan30^\circ=\tfrac{1}{\sqrt3},\ \sin30^\circ=\tfrac12,\ \cot60^\circ=\tfrac{1}{\sqrt3},\ \csc30^\circ=2\).
Step 2: Multiply.
\(\tfrac{1}{\sqrt3}\cdot \tfrac12\cdot \tfrac{1}{\sqrt3}\cdot 2=\tfrac{1}{3}\).