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General solution of tan theta+tan 4 thet...

General solution of `tan theta+tan 4 theta+tan 7 theta=tan theta tan 4 theta tan 7 theta` is

A

`theta=n pi//12`, where `n in Z`

B

`theta=n pi//9`, where `n in Z`

C

`theta = npi+pi//12`, where `n in Z`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
From the given equation, we have
`(tan theta+tan 4 theta)/(1-tan theta tan 4 theta)=-tan 7 theta`
or `tan (theta+4theta)=-tan 7 theta`
or `tan 5 theta = tan (-7theta)`
`rArr 5 theta= n pi -7 theta`
or `theta = npi//12`, where `n in Z`, but `n ne 6, 18, 30`, ...
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