Trigonometric Ratios and Identities
Important Identities
JEE Main 2019
Grade 11
Question:
The value of $\sin 10^\circ \sin 30^\circ \sin 50^\circ \sin 70^\circ$ is:
(1) $\frac{1}{36}$
(2) $\frac{1}{32}$
(3) $\frac{1}{16}$
(4) $\frac{1}{18}$
Step-by-Step Solution
Key Concept: Factor out $\sin 30^\circ = \frac{1}{2}$. Apply the product formula $\sin A \sin(60^\circ - A)\sin(60^\circ + A) = \frac{1}{4} \sin 3A$ with $A = 10^\circ$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)