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Question
Find the general solution of the following equation:
cot 4θ = – 1
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Solution
The general solution of tan θ = tan α is
θ = nπ + α, n ∈ Z
Now,
cot 4θ = – 1
∴ tan 4θ = – 1
∴ tan 4θ = `– tan pi/(4) ...[ ∵ tan pi/4 = 1]`
∴ tan 4θ = `tan(pi - pi/4)` ...[∵ tan(π – θ) = – tan θ]
∴ tan 4θ = `tan (3pi)/(4)`
∴ the required general solution is given by
4θ = `nπ + (3pi)/(4), n ∈ Z`
i.e. θ = `(npi)/(4) + (3pi)/(16),n ∈ Z`.
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