A line makes an angel `theta` with each of the x-and z-axes. If the angel `beta,` which it makes with the y-axis, is such that `sin^2beta=3sin^2theta,t h e ncos^2theta` equals a. `2/3` b. `1/5` c. `3/5` d. `2/5`

Options

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

Answer

c

Explanation

Here `sin^(2)beta=3sintheta" "(i)`
By the question, `cos^(2)theta+cos^(2)theta+cos^(2)beta=1" "(ii)`
`impliescos^(2)beta=1-2cos^(2)theta" "(iii)`
Adding (i) and (iii), we get
`1=1+3sin^(2)theta-2costheta`
`=1+3(1-cos^(2)theta)-2cos^(2)theta`
or `5cos^(2)theta=3`
or `cos^(2)theta=(3)/(5)`