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|{:(1,cos alpha, cos beta),(cos alpha, 1...

`|{:(1,cos alpha, cos beta),(cos alpha, 1,cosgamma),(cosbeta,cosgamma,1):}|=|{:(0,cosalpha,cosbeta),(cosalpha,0,cosbeta),(cosbeta,cosgamma,0):}|`
if `cos^(2)alpha+cos^(2)beta+cos^(2)gamma=`

A

`1`

B

`2`

C

`3//2`

D

`1//2`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `|{:(1,cos alpha, cos beta),(cos alpha, 1,cosgamma),(cosbeta,cosgamma,1):}|=|{:(0,cosalpha,cosbeta),(cosalpha,0,cosbeta),(cosbeta,cosgamma,0):}|`
`impliessin^(2)gamma-cosalpha(cosalpha-cosbetacosgamma)+cosbeta(cosalphacosgamma-cosbeta)`
`=-cosalpha(-cosbetacosgamma)+cosbeta(cosalphacosgamma)`
`impliessin^(2)gamma-cos^(2)alpha+2cosalphacosbetacosgamma-cos^(2)beta=2cosalphacosbetacosgamma`
`impliessin^(2)gamma=cos^(2)alpha+cos^(2)beta`
`impliescos^(2)alpha=cos^(2)beta+cos^(2)gamma=1`
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  • If |{:(1,cos alpha, cos beta),(cos alpha, 1 , cos gamma ),(cos beta, cos gamma , 1):}|=|{:(0,cos alpha, cos beta),(cos alpha , 0 , cos gamma),(cos beta, cos gamma, 0):}| then the value of cos^2 alpha + cos^2 beta + cos^2 gamma is :

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