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JEE Main 2026 · 2 Apr · Shift 1, Mathematics question 11

If sin⁡(π18)sin⁡(5π18)sin⁡(7π18)=K\sin\left(\dfrac\pi{18}\right)\sin\left(\dfrac{5\pi}{18}\right)\sin\left(\dfrac{7\pi}{18}\right)=K, then the value of sin⁡(10Kπ3)\sin\left(\dfrac{10K\pi}3\right) is :

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Answer and worked solution

Official answer: A

Product identity. sin⁡θsin⁡(60∘−θ)sin⁡(60∘+θ)=14sin⁡3θ\sin\theta\sin(60^\circ-\theta)\sin(60^\circ+\theta)=\frac14\sin3\theta. With θ=10∘\theta=10^\circ: K=sin⁡10∘sin⁡50∘sin⁡70∘=14sin⁡30∘=18K=\sin10^\circ\sin50^\circ\sin70^\circ=\frac14\sin30^\circ=\frac18.

Value. sin⁡10Kπ3=sin⁡5π12=sin⁡75∘=3+122\sin\dfrac{10K\pi}3=\sin\dfrac{5\pi}{12}=\sin75^\circ=\dfrac{\sqrt3+1}{2\sqrt2}.

(A)

Topics:Trigonometric ratios and identities
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