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

We need to find the value of the expression \(4 \sin 30^\circ \cos 60^\circ\). Let's solve it step by step:

1. Start by recalling the trigonometric values of the angles involved:
   • \(\sin 30^\circ = \frac{1}{2}\)
   • \(\cos 60^\circ = \frac{1}{2}\)
2. Substitute these trigonometric values into the expression:
   • \(4 \times \sin 30^\circ \times \cos 60^\circ = 4 \times \frac{1}{2} \times \frac{1}{2}\)
3. Simplify the expression by performing the multiplication:
   • \(4 \times \frac{1}{2} \times \frac{1}{2} = 4 \times \frac{1}{4} = 1\)

The value of \(4 \sin 30^\circ \cos 60^\circ\) is therefore found to be 1.

This matches the option: 1