Trigonometrical Equations
easy

જો $2{\tan ^2}\theta = {\sec ^2}\theta , $ તો $\theta $ નો વ્યાપક ઉકેલ મેળવો.

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

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