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General solution of `tan theta+tan 4 theta+tan 7 theta=tan theta tan 4 theta tan 7 theta` isA. `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

Answer» Correct Answer - 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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