if `(3sin^(-1)x+pix-pi)^(2)+{sin(cos^(-1)((x)/(5)))}^(2)-2sin(cos^(-1)((x)/(5)))=-1` then which of the following is/are Correct?

Answer

D

Explanation

From given equation
`(3sin^(-1)x+pix-pi)^(2)+{sin(cos^(-1)((x)/(5))-1}^(2)=0`
Which provide
`3sin^(-1)x+pix-pi=0impliesx=(1)/(2)` .(i)
and `sin(cos^(-1)((x)/(5)))=1`
`impliescos^(-1)((x)/(5))=(pi)/(2)impliesx=0` .. .(ii)
From (i) & (ii) given equation has no solution