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Question
Find the general solution of the following equation:
tan θ = - 1
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Solution
The general solution of tan θ = tan α is
θ = nπ + α, n ∈ Z.
Now, tan θ = – 1
∴ tan θ = - tan `pi/(4) .....[ ∵ tan pi/4 = 1]`
∴ tan θ = `tan(pi - pi/4)` ...[ ∵ tan(π - θ) = – tan θ]
∴ tan θ = `tan (3pi)/(4)`
∴ the required general solution is
θ = nπ + `(3pi)/(4)`, n ∈ Z.
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