The general solution of sin2⁡θsec⁡θ+3tan⁡θ=0is

A
$θ = nπ + (- 1)^{n + 1} \frac{π}{3}, θ = nπ, n \in I$
B
$θ = nπ, n \in I$
C
$θ = nπ + (- 1)^{n + 1} \frac{π}{3}, n \in I$
D
$θ = \frac{nπ}{2}, n \in I$

Solution:

The given equation can be rewritten as

$\begin{array}{l} \tan θ (\sin θ + \sqrt{3}) = 0 \\ \Rightarrow \tan θ = 0 but \sin θ + \sqrt{3} \neq 0 \Rightarrow \tan θ = 0 \\ \Rightarrow θ = nπ, n \in I \end{array}$

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