Trigonometrical Equations
easy

यदि ${\sin ^2}\theta  + \sin \theta  = 2$, तो $\theta $ का व्यापक मान होगा

A

$n\pi + {( - 1)^n}\frac{\pi }{6}$

B

$2n\pi + \frac{\pi }{4}$

C

$n\pi + {( - 1)^n}\frac{\pi }{2}$

D

$n\pi + {( - 1)^n}\frac{\pi }{3}$

Solution

(c) ${\sin ^2}\theta + \sin \theta – 2 = 0$

$\Rightarrow (\sin \theta – 1)\,(\sin \theta + 2) = 0$

$ \Rightarrow $ $\sin \theta \ne – 2$ ,

$\therefore \,\,\sin \theta = 1 = \sin \pi /2$

$ \Rightarrow $ $\theta = n\pi + {( – 1)^n}\frac{\pi }{2}$.

Standard 11
Mathematics

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