The trigonometric equation `sin^(-1)x=2sin^(-1)a` has a solution for all real values (b) `|a|<1/a` `|a|lt=1/(sqrt(2))` (d) `1/2<|a|<1/(sqrt(2))`

Options

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