Question

The value of $4 \sin 30^\circ \cos 60^\circ$ will be :

• A. 1
• B. 1/2
• C. 1/4
• D. 1/8

Hint:

Did you know $\sin 30^\circ$ always equals $\cos 60^\circ$? This is because $\sin \theta = \cos(90^\circ - \theta)$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This problem requires using the standard trigonometric values for $30^\circ$ and $60^\circ$.
Step 2: Substituting Standard Values:
Recall that:
- $\sin 30^\circ = \frac{1}{2}$
- $\cos 60^\circ = \frac{1}{2}$
Step 3: Calculation:
$$4 \times \sin 30^\circ \times \cos 60^\circ$$
$$= 4 \times \left(\frac{1}{2}\right) \times \left(\frac{1}{2}\right)$$
$$= 4 \times \frac{1}{4} = 1$$
Step 4: Final Answer:
The value is 1.