The number of ordered pairs (a,x) satisfying the equation `sec^(2)(a+2)x+a^(2)-1=0, pi lt x lt pi` is

Options

A. 2
B. 1
C. 3
D. infinite

Answer

C

Explanation

We have,
`"sec"^(2) (x+2) y + x^(2)-1 =0`
`rArr "tan"^(2) (x+ 2)y + x^(2) = 0`
`rArr "tan"^(2) (x+ 2) y =0 "and" x =0`
`rArr "tan"^(2)2y = 0 "and " x =0`
`rArr y = 0, (pi)/(2), - (pi)/(2) " and " x = 0`
`therefore (x, y) = (0, 0), (0, pi//2), (0, -pi//2)`
Hence, there are 3 ordered pairs.