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Question
Find the general solution of the following equation:
tan `(2θ)/(3) = sqrt3`.
Solution
The general solution of tan θ = tan α is
θ = nπ + α, n ∈ Z
Now,
tan `(2θ)/(3) = sqrt3`.
∴ tan (2θ)/(3) = tan pi/(3) ...[∵ tan pi/(3) = sqrt(3)]`
∴ the required general solution is given by
`(2θ)/(3) = nπ + pi/(3)`, n ∈ Z.
i.e. θ = `(3npi)/(2) + pi/(2)`, n ∈ Z.
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