Question

Number of ordered pairs (a, x) satisfying the equation ${\sec }^2\left(a+2\right)x+a^2-1=0;-\pi <x<\pi$ is

• A. a = - 3 and b = 1
• B. a = 1 and
• C. and
• D. none of these

Answer 1

The correct option is C and

Given equation ${\sec }^2\left(a+2\right)x+a^2-1=0$ $\Rightarrow {\tan }^2\left(a+2\right)x+a^2=0\Rightarrow {\tan }^2\left(a+2\right)x=0anda=0$ $\Rightarrow {\tan }^{2}2x=0\Rightarrow {\tan }^{2}2x=0\Rightarrow x=0,\frac{\pi }{2},\frac{-\pi }{2}$