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Trigonometrical Equations
easy
यदि $1 + \cot \theta = {\rm{cosec}}\theta $, तो $\theta $ का व्यापक मान है
A
$n\pi + \frac{\pi }{2}$
B
$2n\pi - \frac{\pi }{2}$
C
$2n\pi + \frac{\pi }{2}$
D
इनमें से कोई नहीं
Solution
$\frac{1}{{\sin \theta }} = 1 + \frac{{\cos \theta }}{{\sin \theta }}$
$\Rightarrow \sin \theta + \cos \theta = 1$
$ \Rightarrow $ $\cos \left( {\theta – \frac{\pi }{4}} \right)\, = \cos \frac{\pi }{4} $
$\Rightarrow \theta – \frac{\pi }{4} = 2n\pi \pm \frac{\pi }{4}$
$\therefore $ $\theta = 2n\pi $ या $\theta = 2n\pi + \frac{\pi }{2}$
किन्तु $\theta = 2n\pi $ संभव नहीं है।
Standard 11
Mathematics
