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The value of a for which a x^2+sin^(-1)(...

The value of `a` for which `a x^2+sin^(-1)(x^2-2x+2)+cos^(-1)(x^2-2x+2)=1` has a real solution is `pi/2` (b) `-pi/2` (c) `2/pi` (d) `-2/pi`

A

`(pi)/(2)`

B

`-(pi)/(2)`

C

`(2)/(pi)`

D

`-(2)/(pi)`

Text Solution

Verified by Experts

We have
`x^(2)-2x+2=(x-1)^(2)+1ge1`
So the given equation is menaingful for x=1
putting x=1 we have
`a+sin^(-1)(1)+cos^(1_(1)=0rarra=-(pi)/(2)`
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