Question

The value of $\sin 20^\circ \times \sin 40^\circ \times \sin 60^\circ \times \sin 80^\circ$ is

• A. $\frac{3}{16}$
• B. $\frac{1}{8}$
• C. $\frac{3}{8}$
• D. $\frac{3}{32}$

Hint:

Products of sine functions often simplify using standard trigonometric identities.

Answer 1

The Correct Option is A

Step 1: Use known trigonometric identity.
\[ \sin 20^\circ \sin 40^\circ \sin 60^\circ \sin 80^\circ \]
Step 2: Substitute value of $\sin 60^\circ$.
\[ \sin 60^\circ = \frac{\sqrt{3}}{2} \]
Step 3: Apply product identity.
\[ \sin 20^\circ \sin 40^\circ \sin 80^\circ = \frac{\sqrt{3}}{8} \]
Step 4: Final calculation.
\[ = \frac{\sqrt{3}}{8} \times \frac{\sqrt{3}}{2} = \frac{3}{16} \]