Prove that:cos10∘cos30∘cos50∘cos70∘ =163

We know that 4cosθcos(60o+θ)cos(60o−θ)=cos3θSo,cos10ocos30ocos50ocos70o41 4(cos10ocos30ocos50ocos70o)41 4(cos10ocos(600+100)cos(60o−100)cos30o)=41cos(100×3)×cos30o=163

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Prove that: ,10^{},,30^{},,50^{},,70^{} = {3}{16}

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Prove that:
$cos 1 0^{\circ} cos 3 0^{\circ} cos 5 0^{\circ} cos 7 0^{\circ} = \frac{3}{16}$

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Prove that:

cos 1 0^{\circ} cos 3 0^{\circ} cos 5 0^{\circ} cos 7 0^{\circ} = \frac{3}{16}

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Text solutionVerified

We know that

4 cos θ cos (6 0^{o} + θ) cos (6 0^{o} - θ) = cos 3 θ

S o, cos 1 0^{o} cos 3 0^{o} cos 5 0^{o} cos 7 0^{o}

\frac{1}{4}

4 (cos 1 0^{o} cos 3 0^{o} cos 5 0^{o} cos 7 0^{o})

\frac{1}{4}

4 (cos 1 0^{o} cos (6 0^{0} + 1 0^{0}) cos (6 0^{o} - 1 0^{0}) cos 3 0^{o})

= \frac{1}{4} cos (1 0^{0} \times 3) \times cos 3 0^{o}

= \frac{3}{16}

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Question Text	Prove that: $cos 1 0^{\circ} cos 3 0^{\circ} cos 5 0^{\circ} cos 7 0^{\circ} = \frac{3}{16}$
Answer Type	Text solution:1
Upvotes	150

Prove that:cos10∘cos30∘cos50∘cos70∘ =163​

Text solutionVerified

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Prove that:
$cos 1 0^{\circ} cos 3 0^{\circ} cos 5 0^{\circ} cos 7 0^{\circ} = \frac{3}{16}$