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JEE Main 2019 · 9 Apr · Shift II

JEE Main 2019 Mathematics question on Trigonometry

The value of sin⁡10∘sin⁡30∘sin⁡50∘sin⁡70∘\sin 10^\circ \sin 30^\circ \sin 50^\circ \sin 70^\circ is
  1. A.
    136\dfrac{1}{36}
  2. B.
    132\dfrac{1}{32}
  3. C.
    116\dfrac{1}{16}
  4. D.
    118\dfrac{1}{18}
Show answer and solution

Correct option: C

Solution

Use the identity: sin θ · sin(60°−θ) · sin(60°+θ) = (1/4)sin 3θ.

Set θ = 10°: sin 10° · sin 50° · sin 70° = (1/4)sin 30° = (1/4)(1/2) = 1/8.

Multiply by sin 30° = 1/2: sin 10° · sin 30° · sin 50° · sin 70° = (1/8)(1/2) = 1/16.

[JEE Main 2019 · 9 Apr · Shift II]

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