JEE PYQ: Trigonometric Ratios And Identities Question 10
Question 10 - 2019 (09 Apr Shift 2)
The value of $\sin 10° \sin 30° \sin 50° \sin 70°$ is:
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(1) $\frac{1}{16}$
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(2) $\frac{1}{32}$
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(3) $\frac{1}{18}$
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(4) $\frac{1}{36}$
Show Answer
Answer: (1) $\frac{1}{16}$
Solution
Using $\sin A \sin(60°-A)\sin(60°+A) = \frac{1}{4}\sin 3A$: $\sin 10° \sin 50° \sin 70° = \frac{1}{4}\sin 30°$. Multiply by $\sin 30° = \frac{1}{2}$: result $= \frac{1}{16}$.
BETA
