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Trigonometrical Equations
medium
If $\cos 2\theta + 3\cos \theta = 0$, then the general value of $\theta $ is
A
$2n\pi \pm {\cos ^{ - 1}}\frac{{ - 3 + \sqrt {17} }}{4}$
B
$2n\pi \pm {\cos ^{ - 1}}\frac{{ - 3 - \sqrt {17} }}{4}$
C
$n\pi \pm {\cos ^{ - 1}}\frac{{ - 3 + \sqrt {17} }}{4}$
D
$n\pi \pm {\cos ^{ - 1}}\frac{{ - 3 - \sqrt {17} }}{4}$
Solution
(a) $2{\cos ^2}\theta – 1 + 3\cos \theta = 0$
$\cos \theta = \frac{{ – 3 \pm \sqrt {9 + 8} }}{4} = \frac{{ – 3 \pm \sqrt {17} }}{4}$
$ \Rightarrow $ $\theta = 2n\pi \pm {\cos ^{ – 1}}\left( {\frac{{ – 3 + \sqrt {17} }}{4}} \right)$, (Taking $+ve$ sign).
Standard 11
Mathematics
