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If $\tan 5 θ = \cot 2 θ then θ =$ ______

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a

$θ = \frac{nπ}{7} + \frac{π}{14}; n \in Z$

b

$θ = \frac{nπ}{14} - \frac{π}{7}; n \in Z$

c

$θ = \frac{nπ}{7} - \frac{π}{14}; n \in Z$

d

$θ = \frac{nπ}{14} + \frac{π}{7}; n \in Z$

answer is A.

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Detailed Solution

$\begin{array}{l} \tan 5 θ = \cot 2 θ = \tan (\frac{π}{2} - 2 θ) \\ \Rightarrow 5 θ = nπ + \frac{π}{2} - 2 θ \Rightarrow 7 θ = nπ + \frac{π}{2} \\ \Rightarrow θ = \frac{nπ}{7} + \frac{π}{14}, where n \in Z, but n \neq 3, 10, 17, \dots \end{array}$
where tan 5 $θ$ is not defined.

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If tan⁡5θ=cot⁡2θ then θ=______