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If a line in the space makes angle alpha...

If a line in the space makes angle `alpha,beta and gamma` with the coordinate axes, then `cos2alpha+cos2beta+cos2gamma+sin^2alpha+sin^2beta+sin^2gamma` equals

A

`-1`

B

`0`

C

`1`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
C
`cos2alpha+cos2beta+cos2gamma+sin^2alpha+sin^2beta+sin^2gamma`
`=(cos^2alpha-sin^2alpha)+(cos^2beta-sin^2beta)+(cos^2gamma-sin^2gamma)+sin^2alpha+sin^2beta+sin^2gamma`
`=cos^2alpha+cos2^beta+cos^2gamma=1`
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