Trigonometric Equations Question 78
Question: The smallest positive angle which satisfies the equation $ 2{{\sin }^{2}}\theta +\sqrt{3}\cos \theta +1=0 $ , is
[ISM Dhanbad 1972; MP PET 1993]
Options:
A) $ \frac{5\pi }{6} $
B) $ \frac{2\pi }{3} $
C) $ \frac{\pi }{3} $
D) $ \frac{\pi }{6} $
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Answer:
Correct Answer: A
Solution:
- $ 2-2{{\cos }^{2}}\theta +\sqrt{3}\cos \theta +1=0 $
$ \Rightarrow $ $ 2{{\cos }^{2}}\theta -\sqrt{3}\cos \theta -3=0 $
$ \Rightarrow $ $ \cos \theta =\frac{\sqrt{3}\pm \sqrt{3+24}}{4}=\frac{\sqrt{3}(1\pm 3)}{4}=\sqrt{3}( -\frac{1}{2} ) $
$ \Rightarrow $ $ \theta =\frac{5\pi }{6} $ .
BETA
