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Question
Find the principal solution of the following equation:
tan θ = – 1
Solution
We know that,
`tan pi/(4) = 1 and tan (pi - θ)` = – tan θ,
tan (2π – θ) = – tanθ
∴ `tan(pi - pi/4) = - tan pi/(4)` = - 1
and `tan(2pi - pi/4) = -tan pi/(4)` = – 1
∴ `tan (3pi)/(4) = tan (7pi)/(4)` = – 1, where
`0 < (3pi)/(4) < 2pi and 0 < (7pi)/(4) < 2pi`
∴ tan θ = – 1 gives,
tan θ = `tan (3pi)/(4) = tan (7pi)/(4)`
∴ θ = `(3pi)/(4)` and θ = `(7pi)/(4)`
Hence, the required principal solutions are
θ = `(3pi)/(4)` and θ = `(7pi)/(4)`.
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