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Question
Find the principal solution of the following equation:
cot θ = 0
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Solution
The given equation is cot θ = 0 which is same as
tan θ = ∞
We know that,
tan `π/2` = ∞ and tan (π + θ) = tan θ
∴ `tan (π/2) = tan (π + π/2) = tan ((3π)/2)`
∴ `tan (π/2) = tan ((3π)/2) = ∞`, where,
`0 < π/2 < 2π and 0 < (3π)/2 < 2π`
∴ cot θ = 0, i.e., tan θ = ∞ gives
`tan θ = tan (π/2) = tan ((3π)/2)`
∴ `θ = π/2 "and" θ = (3π)/2`
Hence, the required principal solution are `θ = π/2 "and" θ = (3π)/2`.
Notes
Answer in the textbook is incorrect.
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