A line makes the same angle `theta` with X-axis and Z-axis. If the angle `beta`, which it makes with Y-axis, is such that `sin^2(beta)=3sin^2theta`, then the value of `cos^(2)theta` is

Options

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

Answer

C

Explanation

Let `l,m,n` be the direction `cos` (lies. Then,
`l=cos theta,m=cos beta` and `n=cos theta`
`impliesl^(2)+m^(2)+n^(2)=1`
`impliescos^(2)theta+cos^(2)beta+cos^(2) theta=1`
`implies2cos^(2)theta+1-sin^(2)beta=1implies2cos^(2)theta-sin^(2)beta=0`
`implies2cos^(2)theta-3sin^(2)theta=0 [ sin^(2) beta=3 sin^(2)theta` (Given )`]`
`impliestan^(2)theta=2/3`
`:.cos^(2)theta=1/(1+tan^(2)theta)=1/(1+2//3)=3/5`