`|{:(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=`

Options

A. `1`
B. `2`
C. `3//2`
D. `1//2`

Answer

A

Explanation

`(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`