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← JEE Main 2022 · 26 Jun · Shift 2
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JEE Main 2022 · 26 Jun · Shift 2, Mathematics question 18

16sin⁡(20°)sin⁡(40°)sin⁡(80°)16\sin(20°)\sin(40°)\sin(80°) is equal to :

Choose one option
Answer and worked solution

Official answer: B

Identity. sin⁡θsin⁡(60°−θ)sin⁡(60°+θ)=14sin⁡3θ\sin\theta\sin(60°-\theta)\sin(60°+\theta)=\frac14\sin3\theta with θ=20°\theta=20°: sin⁡20sin⁡40sin⁡80=14sin⁡60°=38\sin20\sin40\sin80=\frac14\sin60°=\frac{\sqrt3}8.

Value. 16×38=2316\times\frac{\sqrt3}8=2\sqrt3.

(B)

Topics:Trigonometric ratios and identities
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