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If a line makes angles `alpha,beta,gamma` with the positive direction of coordinate axes, then write the value of `sin^2alpha+sin^2beta+sin^2gammadot`

A

1

B

2

C

0

D

-1

Text Solution

Verified by Experts

The correct Answer is:
B
Given expressio, `sin ^(2)alpha +sin ^(2)beta+sin ^(2)gamma`
`=(1-cos ^(2)alpha)+(1-cos^(2)beta)+(1-cos ^(2)gamma)`
`=3-cos ^(2)alpha+cos ^(2)beta+cos ^(2)gamma=3-1=2`
`(becausecos ^(2)alpha+cos ^(2)beta+cos ^(2)gamma=1)`
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