If `sin^(-1)x+cot^(-1)((1)/(2))=(pi)/(2),` then x is equalt to

Options

A. R
B. `[-1, 1]`
C. `[0, 1]`
D. `phi`

Answer

C

Explanation

`|sin^(-1) x| + |cos^(-1) x| = (pi)/(2)`
`rArr |sin^(-1)x | + cos^(-1) x = (pi)/(2)` ( `:' cos^(-1) x` is always non-negative)
`rArr |sin^(-1) x| = sin^(-1) x`
`rArr sin^(-1) x ge 0`
`rArr 0 le sin^(-1) x le (pi)/(2)`
`rArr 0 le x le 1`