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

Options

A. `-1`
B. 0
C. 1
D. 2

Answer

C

Explanation

`cos2 alpha+cos2beta+cos2gamma+sin^(2)alpha+sin^(2)beta+sin^(2)gamma`
`=(cos^(2)alpha-sin^(2)alpha)+(cos^(2)beta-sin^(2)beta)+(cos^(2)gamma-sin^(2)gamma)+sin^(2)alpha+sin^(2)beta+sin^(2)gamma`
`=cos^(2)alpha+cos^(2)beta+cos^(2)gamma=1`