If the equation`2^((2pi)/cos^(-1)x)-(a+1/2)2^((pi)/cos^(-1)x-a^2=0` has exactly one real solution the range of `a` is equal to

Options

A. `(-3, 1)`
B. `(-oo,-3]`
C. `[1,oo)`
D. `[-3,oo)`

Answer

B, C

Explanation

Let `2^((pi)/(cos^(-1)x))=timpliestge2`
`:.` equation becomes `t^(2)-(a+1/2)t-a^(2)=0`
has one root 2 or greater than 2 & other root less than `2impliesf(2)le0`
`implies4-(a+1/2):2-a^(2)le0`
`a^(2)+2a-3ge0`
`(a+3)(a-1)ge0`
`impliesale-3` or `age1`