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Trigonometrical Equations
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સમીકરણ ${\sin ^2}\theta \sec \theta + \sqrt 3 \tan \theta = 0$ નો વ્યાપક ઉકેલ મેળવો.
A
$\theta = n\pi + {( - 1)^{n + 1}}\frac{\pi }{3},\theta = n\pi ,n \in Z$
B
$\theta = n\pi ,n \in Z$
C
$\theta = n\pi + {( - 1)^{n + 1}}\frac{\pi }{3},n \in Z$
D
$\theta = \frac{{n\pi }}{2},n \in Z$
Solution
(b) The given equation can be written as
$ \Rightarrow $$\frac{{{{\sin }^2}\theta }}{{\cos \theta }} + \sqrt 3 \tan \theta = 0$
$ \Rightarrow $ $\tan \theta \sin \theta + \sqrt 3 \tan \theta = 0$
$\tan \theta (\sin \theta + \sqrt 3 ) = 0$
$ \Rightarrow $ $\tan \theta = 0$
$ \Rightarrow $$\theta = n\pi ,\,n \in Z$.
Standard 11
Mathematics
