New user? Sign up

Existing user? Log in

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 2 years, 1 month ago

Easy Math Editor

*italics*

_italics_

**bold**

__bold__

- bulleted- list

1. numbered2. list

paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)

> This is a quote

This is a quote

# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

2 \times 3

2^{34}

a_{i-1}

\frac{2}{3}

\sqrt{2}

\sum_{i=1}^3

\sin \theta

\boxed{123}

Sort by:

\(\text{We have } \sin{\alpha}+\sin{\beta}+\sin{\gamma}=3 , \text{ since } -1\le \sin{\theta}\le 1\\ \text{We can conclude that } \sin{\alpha}=\sin{\beta}=\sin{\gamma}=1 \implies \cos{\alpha}=\cos{\beta}=\cos{\gamma} = 0 \\ \implies \cos^3{\alpha}+\cos^9{\beta}+\cos^{27}{\gamma} =\boxed{0}\)

Log in to reply

0

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.

Problem Loading...

Note Loading...

Set Loading...

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewest\(\text{We have } \sin{\alpha}+\sin{\beta}+\sin{\gamma}=3 , \text{ since } -1\le \sin{\theta}\le 1\\ \text{We can conclude that } \sin{\alpha}=\sin{\beta}=\sin{\gamma}=1 \implies \cos{\alpha}=\cos{\beta}=\cos{\gamma} = 0 \\ \implies \cos^3{\alpha}+\cos^9{\beta}+\cos^{27}{\gamma} =\boxed{0}\)

Log in to reply

0

Log in to reply

Explain your working please.

Log in to reply

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.

Log in to reply

0

Log in to reply