Question

If $4{\sec }^{2}x=7+{\tan }^{2}x$ , then $x$ is equal to

• A. $n\pi \pm \frac{\pi }{4},n\in Z$
• B. $n\pi \pm \frac{\pi }{6},n\in Z$
• C. $n\pi \pm \frac{\pi }{2},n\in Z$
• D. $n\pi \pm \frac{\pi }{3},n\in Z$

Answer 1

The correct option is A $n\pi \pm \frac{\pi }{4},n\in Z$

$4{\sec }^{2}x=7+{\tan }^{2}x\Rightarrow 4(1+{\tan }^{2}x)=7+{\tan }^{2}x\Rightarrow 3{\tan }^{2}x=3\Rightarrow {\tan }^{2}x=1={\tan }^2\frac{\pi }{4}\Rightarrow x=n\pi \pm \frac{\pi }{4},n\in Z$