The trigonometric equation `sin^(-1)x=2sin^(-1)a` has a solution for all real values

Options

A. all real values
B. `|a| lt (1)/(2)`
C. `|a| le (1)/(sqrt2)`
D. `2 lt |a| lt (1)/(sqrt2)`

Answer

C

Explanation

`sin^(-1) x = 2 sin^(-1) a`
Now `-(pi)/(2) le sin^(-1) a le(pi)/(2)`
`rArr -(pi)/(4) le sin^(-1) a le (pi)/(4)`
`rArr -(1)/(sqrt2) le a le (1)/(sqrt2)`
`rArr |a| le (1)/(sqrt2)`