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Trigonometrical Equations
easy
If $2{\tan ^2}\theta = {\sec ^2}\theta ,$ then the general value of $\theta $ is
A
$n\pi + \frac{\pi }{4}$
B
$n\pi - \frac{\pi }{4}$
C
$n\pi \pm \frac{\pi }{4}$
D
$2n\pi \pm \frac{\pi }{4}$
Solution
(c) $2{\tan ^2}\theta = {\sec ^2}\theta$
$\Rightarrow 2{\tan ^2}\theta = {\tan ^2}\theta + 1$
$ \Rightarrow $ ${\tan ^2}\theta = 1 = {\tan ^2}\left( {\frac{\pi }{4}} \right)$
$\Rightarrow \theta = n\pi \pm \frac{\pi }{4}$.
Standard 11
Mathematics
