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Trigonometrical Equations
easy
If $1 + \cot \theta = {\rm{cosec}}\theta $, then the general value of $\theta $ is
A
$n\pi + \frac{\pi }{2}$
B
$2n\pi - \frac{\pi }{2}$
C
$2n\pi + \frac{\pi }{2}$
D
None of these
Solution
(c) $\frac{1}{{\sin \theta }} = 1 + \frac{{\cos \theta }}{{\sin \theta }}$
$\Rightarrow \sin \theta + \cos \theta = 1$
$ \Rightarrow $ $\cos \left( {\theta – \frac{\pi }{4}} \right)\, = \cos \frac{\pi }{4} $
$\Rightarrow \theta – \frac{\pi }{4} = 2n\pi \pm \frac{\pi }{4}$
Hence $\theta = 2n\pi $ or $\theta = 2n\pi + \frac{\pi }{2}$.
But $\theta = 2n\pi $ is ruled out.
Standard 11
Mathematics
