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Trigonometrical Equations
easy
यदि $\cos \theta + \sec \theta = \frac{5}{2}$, तो $\theta $ का व्यापक मान है
A
$n\pi \pm \frac{\pi }{3}$
B
$2n\pi \pm \frac{\pi }{6}$
C
$n\pi \pm \frac{\pi }{6}$
D
$2n\pi \pm \frac{\pi }{3}$
Solution
${\cos ^2}\theta – \frac{5}{2}\cos \theta + 1 = 0$
$ \Rightarrow $ $\cos \theta = \frac{{(5/2) \pm \sqrt {(25/4) – 4} }}{2} = \frac{{5 \pm 3}}{4}$
$(+)$ चिन्ह की उपेक्षा करने पर,
$ \Rightarrow $ $\cos \theta = \frac{1}{2} = \cos \left( {\frac{\pi }{3}} \right)$
$\Rightarrow \theta = 2n\pi \pm \frac{\pi }{3}$.
Standard 11
Mathematics
