∏ j = m n cos ( 2 j θ ) = 2 n − m + 1 s i n ( 2 m θ ) s i n ( 2 n + 1 θ ) when defined. Evaluate sin ( 9 π /14 ) sin ( 11 π /14 ) sin ( 13 π /14 ) .

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Mathematics - Trigonometric Equation Question with Solution | TestHub

MathematicsTrigonometric EquationTrigonometric EquationMedium2 minInstinct batch 2026-09-29

MathematicsMediumsingle choice

$\prod_{j = m}^{n} cos (2^{j} θ) = \frac{s i n ( 2 ^{n + 1} θ )}{2 ^{n - m + 1} s i n ( 2 ^{m} θ )}$ when defined. Evaluate $sin (9 π /14) sin (11 π /14) sin (13 π /14)$ .

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Answer:

Solution:

By supplementary angles the product equals sin(5π/14) sin(3π/14) sin(π/14) = cos(π/7) cos(2π/7) cos(3π/7) = 1/8.

Stream:JEESubject:MathematicsTopic:Trigonometric EquationSubtopic:Trigonometric Equation

⏱ 2mℹ️ Source: Instinct batch 2026-09-29

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