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If (sin^(-1)x)^(2)+(cos^(-1)x)^(2)=(5pi^...

If `(sin^(-1)x)^(2)+(cos^(-1)x)^(2)=(5pi^(2))/(8)` then x =

A

`-2`

B

`-3`

C

`-1`

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
Given , `(tan^(1)x)^(2)+(cot^(-1)x)^(2)=(5pi^(2))/(8)`
`rArr(tan^(-1)x+cot^(-1)x)^(2)-2tan^(-1)x*cot^(-1)x=(5pi^(2))/(8)`
`rArr((pi)/(2))^(2)-2tan^(-1)x((pi)/(2)-tan^(-1)x)=(5pi^(2))/(8)`
`rArr(pi^(2))/(4)-2*(pi)/(2)tan^(-1)x+2(tan^(-1)x)^(2)=(5pi^(2))/(8)`
`rArr2(tan^(-1)x)^(2)-pitan^(-1)x-(3pi^(2))/(8)=0`
`rArr16(tan^(-1)x)^(2)-8pitan^(-1)x-3pi^(2)=0`
`rArr16(tan^(-1)x)^(2)-12pitan^(-1)x+4pitan^(-1)x-3pi^(2)=0`
`rArr4(tan^(-1)x)[4tan^(-1)x-3pi]+pi(4tan^(-1)x-3pi)=0`
`rArr(4tan^(-1)x+pi)(4tan^(-1)x-3pi)=0`
`rArrtan^(-1)x=-(pi)/(4),(3pi)/(4)`
`rArrtan^(-1)x=-(pi)/(4)`
`rArr x=-1`
{neglecting `tan^(-1)x=(3pi)/(4(as tan^9-1)xin[-(pi)/(2),(pi)/(2)]}`
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