If + + = 3, then ^3 + ^3 + ^3 will be Option 1: 2 Option 2: 1 Option 3: 3 Option 4: 0

Answer: 3. Solution: The maximum value of is 1 for any angle . So the maximum possible value of + + is 1 + 1 + 1 = 3. Since + + = 3, each term must be at its maximum value. = = = 1 ^3 + ^3 + ^3 = 1^3 + 1^3 + 1^3 = 3

Geometry

Trigonometry

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If $\cos\alpha + \cos\beta + \cos\gamma = 3$ , then $\cos^3\alpha + \cos^3\beta + \cos^3\gamma$ will be

✅ Correct Option: 3

The maximum value of $\cos\theta$ is $1$ for any angle $\theta$ .

So the maximum possible value of $\cos\alpha + \cos\beta + \cos\gamma$ is $1 + 1 + 1 = 3$ .

Since $\cos\alpha + \cos\beta + \cos\gamma = 3$ , each term must be at its maximum value.

$\cos\alpha = \cos\beta = \cos\gamma = 1$

$\cos^3\alpha + \cos^3\beta + \cos^3\gamma$

$= 1^3 + 1^3 + 1^3$

$= 3$

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If cos⁡α+cos⁡β+cos⁡γ=3\cos\alpha + \cos\beta + \cos\gamma = 3cosα+cosβ+cosγ=3, then cos⁡3α+cos⁡3β+cos⁡3γ\cos^3\alpha + \cos^3\beta + \cos^3\gammacos3α+cos3β+cos3γ will be

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If $\cos\alpha + \cos\beta + \cos\gamma = 3$ , then $\cos^3\alpha + \cos^3\beta + \cos^3\gamma$ will be