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If tan^(-1)(x^(2)+3|x|-4)+cot^(-1)(4pi+s...

If `tan^(-1)(x^(2)+3|x|-4)+cot^(-1)(4pi+sin^(-1)sin14)=(pi)/(2)`, then the value of `sin^(-1)(sin2x)` can be equal to

A

`6-2pi`

B

`2pi-6`

C

`pi-3`

D

`3-pi`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`tan^(-1)(x^(2)+3|x|-4)+cot^(-1)(4pi+sin^(-1)sin^(1)4)=(pi)/(2)`
`impliestan^(-1)(x^(2)+3|x|-4)+cot^(-1)(4pi+14-4pi)=(pi)/(2)`
`impliesx^(2)+3|x|-4=14impliesx^92)+6|x|-3|x|-18=0`
`(|x|+6)((|x|-3)=0,impliesx=+-3`
So, `sin^(-1)sin2x=sin^(-1)sin6` or `sin^(-1)sin(-6)=6-2pi` or `2pi-6`
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