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Trigonometrical Equations
easy
यदि $\tan \theta - \sqrt 2 \sec \theta = \sqrt 3 $, तो $\theta $ का व्यापक मान है
A
$n\pi + {( - 1)^n}\frac{\pi }{4} - \frac{\pi }{3}$
B
$n\pi + {( - 1)^n}\frac{\pi }{3} - \frac{\pi }{4}$
C
$n\pi + {( - 1)^n}\frac{\pi }{3} + \frac{\pi }{4}$
D
$n\pi + {( - 1)^n}\frac{\pi }{4} + \frac{\pi }{3}$
Solution
(d) $\tan \theta – \sqrt 2 \sec \theta = \sqrt 3$
$\Rightarrow \sin \theta – \sqrt 3 \cos \theta = \sqrt 2 $
$ \Rightarrow $ $\sin \left( {\theta – \frac{\pi }{3}} \right) = \sin \frac{\pi }{4}$
$\Rightarrow \theta = n\pi + {( – 1)^n}\frac{\pi }{4} + \frac{\pi }{3}$.
Standard 11
Mathematics
