A line line makes the same angle `theta` with each of the `x` and z-axes. If the angle `beta`, which it makes with y-axis, is such that `sin^(2)beta=3sin^(2)theta` then `cos^(2)theta` equals

Options

A. `2//3`
B. `1//5`
C. `3//5`
D. `2//5`

Answer

C

Explanation

Since, `l^(2)+m^(2)+n^(2)=1`
`cos^(2)theta +cos^(2)beta+cos^(2)theta=1`
` " " [because l=cos theta, m=cos beta, " given"]`
`rArr 2 cos^(2)theta=sin^(2)beta`
But `sin^(2) beta=3 sin^(2) theta`
`therefore 3sin^(2)theta =2 cos^(2)theta`
`rArr 3= 5 cos^(2)theta`
`rArr cos^(2)theta=(3)/(5)`