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If cos alpha + cos beta + cos gamma = ...

If ` cos alpha + cos beta + cos gamma = 0 sin alpha + sin beta + sin gamma ` , Prove that
`cos^(2) alpha + cos^(2) beta + cos^(2) gamma = 3/2 = sin^(2) alpha + sin^(2) beta + sin^(2) gamma`.

Text Solution

Verified by Experts

The correct Answer is:
`3/2`
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Knowledge Check

  • cos alpha + cos beta + cos gamma + cos ( alpha + beta + gamma ) =

    A
    `4 sin""((alpha + beta )/(2))* cos""((beta + gamma )/(2)) * cos ((gamma + alpha )/(2))`
    B
    `4 cos""((alpha + beta )/(2)) * cos""((beta + gamma )/(2)) * cos ""((gamma + alpha )/(2))`
    C
    `4 sin""((alpha + beta )/(2))* sin ((beta + gamma )/(2)) * sin""(( gamma + alpha )/(2))`
    D
    `4 cos ""((alpha + beta )/(2)) * cos""((beta + gamma )/(2))* sin""((gamma + alpha )/(2))`

  • If cos alpha + cos beta =0 = sin alpha + sin beta " then " cos (alpha - beta )=

    A
    0
    B
    `1`
    C
    `-1`
    D
    2

  • I : If cos alpha + cos beta + cos gamma =3 " then " sin alpha + sin beta + sin gamma =0 II : If sin alpha + sin beta + sin gamma =3 " then " cos alpha + cos beta + cos gamma =0

    A
    only I is true
    B
    only II is true
    C
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    D
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