Question

The value of \( 2\sin30^\circ \cos30^\circ \) is:

• A. 1
• B. $\dfrac{1}{2}$
• C. $\sqrt{3}$
• D. $\dfrac{\sqrt{3}}{2}$

Hint:

Always remember: \( 2\sin A \cos A = \sin(2A) \). It helps simplify many trigonometric expressions quickly.

Answer 1

The Correct Option is D

Step 1: Recall the identity.
\[ 2\sin A \cos A = \sin(2A) \]
Step 2: Substitute \( A = 30° \).
\[ 2\sin30° \cos30° = \sin(60°) \]
Step 3: Value of \( \sin60° \).
\[ \sin60° = \frac{\sqrt{3}}{2} \]
Step 4: Conclusion.
Hence, \( 2\sin30°\cos30° = \boxed{\frac{\sqrt{3}}{2}} \).