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

Question

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

`|{:(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`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - 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`