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

`2/3`

`1/5`

`3/5`

`2/5`

Solution

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Here `sin^2beta = 3sin^2theta` ...........(1)

By the question `cos^2theta + cos^2theta + cos^2beta= 1` ..........(2)

`cos^2beta = 1 – 2 cos^2theta` ..........(3)

Adding (1) and (3), we get

`1 = 1 + 3 sin^2theta – 2cos^2theta`

`1 =1 + 3(1 – cos^2theta) – 2cos^2theta`

`5cos^2 theta=2`

`cos^2theta =2/5`