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`,then `cos^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)`

Explanation

To solve the problem step by step, we will use the relationships between the angles and the direction cosines of the line.

### Step 1: Define the direction cosines
Let the direction cosines of the line be:
- \( l = \cos \theta \) (with the x-axis)
- \( m = \cos \beta \) (with the y-axis)
- \( n = \cos \theta \) (with the z-axis)

...