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Number of ordered pairs (a, x) satisfyin...

Number of ordered pairs (a, x) satisfying the equation `sec^2(a+2)x+a^2-1=0;-pi < x< pi` is

A

2

B

1

C

3

D

infinite

Text Solution

Verified by Experts

The correct Answer is:
C
We have `sec^(2)(a+2)x=1-a^(2)`
Now `sec^(2)x ge 1`
`rArr 1-alpha^(2)ge 1`
`rArr a = 0`
So, `sec^(2)(a+2)x = 1`
`rArr sec^(2)2x = 1`
`rArr x=-(pi)/(2), 0,(pi)/(2)`
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