The number of ordered pairs a , x satisfying the equation sec 2 ⁡ a + 2 x + a 2 - 1 = 0 ,   - π < x < π is

Step-by-step solution

Given equation is sec 2 ⁡ a + 2 x + a 2 - 1 = 0 ⇒ tan 2 ⁡ a + 2 x + a 2 = 0 ⇒ tan ⁡ a + 2 x = 0 and a = 0 ⇒ tan ⁡ 2 x = 0 ⇒ x = 0 , π 2 , - π 2 . So, 0 , 0 , 0 , π 2 , 0 , - π 2 are ordered pairs a , x satisfying the equation.