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Question
Find the general solutions of the following equation:
`tan theta = - sqrt3`
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Solution
The general solution of tan θ = tan α is
θ = nπ + α, n ∈ Z.
Now, tan θ = - `sqrt3`
∴ tan θ = - `tan pi/3 ....[because "tan" pi/3 = sqrt3]`
∴ tan θ = tan`(pi - pi/3) ...[because tan (pi - theta) = - tan theta]`
∴ tan θ = tan`(2pi)/3`
∴ the required general solution is
∴ θ = `"n"pi + (2pi)/3,` n ∈ Z
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