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A line makes an angle theta both with x-...

A line makes an angle `theta` both with x-axis and y-axis. A possible range of `theta` is

A

`[0,pi/4]`

B

`[0,pi/2]`

C

`[pi/4,pi/2]`

D

`[pi/3,pi/6]`

Text Solution

Verified by Experts

The correct Answer is:
C
We know that `cos^(2)alpha=cos^(2)beta+cos^(2)gamma=1`
`Rightarrow cos^(2)theta=cos^(2)theta+cos^(2)gamma=1" "[therefore alpha=beta=theta]`
`Rightarrow 2 cos^(2)theta+cos^(2)gamma=1`
`Rightarrow cos^2gamma=1-2cos^(2)theta`
`Rightarrow cos^2gamma=-cos^(2)theta`
`Rightarrow cos 2theta le theta`
`therefore theta in [pi/4,pi/2]`
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