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If a line makes angles alpha, beta, gamm...

If a line makes angles `alpha, beta, gamma` with the coordinate axes, prove that `sin^2alpha+sin^2beta+sin^2gamma=`

A

`0`

B

`1`

C

`2`

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
C
`thereforesin^2alpha+sin^2beta+sin^2gamma`
`=(1-cos^2alpha)+(1-cos^2beta)+(1-cos^2gamma)`
`=3-(cos^2alpha+cos^2beta+cos^2gamma)=3-1=2`
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