A 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`=

Options

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

Answer

C

Explanation

Since `l^2+m^2+n^2=1`
`rArr" "cos^2theta+cos^2beta+cos^2theta=1" "[thereforel=costheta,m=cosbeta and n=costheta" given"]`
`rArr" "2cos^2theta=sin^2beta" "[therefore1-cos^2beta=sin^2beta]`
But `sin^2beta=3sin^2theta`
`therefore" "3sin^2theta=2cos^2theta`
`rArr" "3=5cos^2theta`
`rArr" "cos^2theta=3/5`