The product of all values of `x` satisfying the equation `sin^(-1)cos((2x^2+10|x|+4)/(x^2+5|x|+3))=cot(cot^(-1)((2-18|x|)/(9|x|)))+pi/2 ` is (a)9 (b) `-9` (c) `-3` (d) `-1`

Options

A. 9
B. `-9`
C. `-3`
D. `-1`

Answer

A

Explanation

`(pi)/(2) - cos^(-1) cos ((2(x^(2) + 5|x| + 3) -2)/(x^(2) + 5|x| + 3))`
`= cot cot^(-1) ((2)/(9|x|) -2) + (pi)/(2)`
`rArr (pi)/(2) -2 + (2)/(x^(2) + 5|x| + 3) = (2)/(9|x|) -2 + (pi)/(2)`
`rArr |x|^(2) - 4 |x| + 3 = 0`
`rArr |x| = 1, 3 " or " x = +- 1, +- 3`