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If 3(cos 2phi-cos2theta)=1-cos2phi cos2t...

If `3(cos 2phi-cos2theta)=1-cos2phi cos2theta`, then `tan theta= k tan phi`, where `theta, phiin (0,(pi)/(2))`, where k =

A

`sqrt(2)`

B

`(1)/(sqrt(2))`

C

`sqrt(3)`

D

`(1)/(sqrt(3))`

Text Solution

Verified by Experts

The correct Answer is:
A
`3 cos 2phi-3 cos 2theta =1-cos 2phi cos 2 theta`
`rArr (3+cos 2theta) cos 2phi =1+3 cos 2theta`
`rArr cos 2 phi = (1+3 cos 2theta)/(3+cos 2theta)`
`rArr (1-cos 2phi)/(1+cos 2phi)=(1)/(2).(1-cos 2theta)/(1+cos 2theta)` (using componendo and dividendo)
`rArr tan^(2) phi = (1)/(2) tan^(2) theta`
`rArr tan theta = sqrt(2) tan phi`
`rArr k = sqrt(2)`
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