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If \(\sin\alpha + \sin\beta + \sin \gamma = 3 \), fidn the value of \(\cos^3 \alpha + \cos^9 \beta + \cos^{27} \gamma \).
Note by Pritthijit Nath 1 year, 11 months ago
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2 \times 3
2^{34}
a_{i-1}
\frac{2}{3}
\sqrt{2}
\sum_{i=1}^3
\sin \theta
\boxed{123}
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\(\text{We have } \sin{\alpha}+\sin{\beta}+\sin{\gamma}=3 , \text{ since } -1\le \sin{\theta}\le 1\\ \text{We can conclude that } \sin{\alpha}=\sin{\beta}=\sin{\gamma}=1 \implies \cos{\alpha}=\cos{\beta}=\cos{\gamma} = 0 \\ \implies \cos^3{\alpha}+\cos^9{\beta}+\cos^{27}{\gamma} =\boxed{0}\)
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Explain your working please.
Max . Value of sum of three sines = 3 , since (-1 < sin¤ < +1)
Equality is there in both.,
Therefore we conclude that maximum value (=3) occurs when, all three sines are equal & hence 1.
Therefore cosines will be all 0 , Nd hence the given sum will be equal to zero.
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*italics*
or_italics_
**bold**
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paragraph 1
paragraph 2
[example link](https://brilliant.org)
> This is a quote
2 \times 3
2^{34}
a_{i-1}
\frac{2}{3}
\sqrt{2}
\sum_{i=1}^3
\sin \theta
\boxed{123}
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Top Newest\(\text{We have } \sin{\alpha}+\sin{\beta}+\sin{\gamma}=3 , \text{ since } -1\le \sin{\theta}\le 1\\ \text{We can conclude that } \sin{\alpha}=\sin{\beta}=\sin{\gamma}=1 \implies \cos{\alpha}=\cos{\beta}=\cos{\gamma} = 0 \\ \implies \cos^3{\alpha}+\cos^9{\beta}+\cos^{27}{\gamma} =\boxed{0}\)
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Explain your working please.
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Max . Value of sum of three sines = 3 , since (-1 < sin¤ < +1)
Equality is there in both.,
Therefore we conclude that maximum value (=3) occurs when, all three sines are equal & hence 1.
Therefore cosines will be all 0 , Nd hence the given sum will be equal to zero.
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