The soluation set of inequality `(sinx+cos^(- 1)x)-(cosx-sin^-1x)>= pi/2,` is equal to

Options

A. `[(pi)/(4),(5pi)/(4)]`
B. `uuu_(n in I)[2n pi+(pi)/(4),2n pi+(5pi)/(4)]`
C. `[(pi)/(4),1]`
D. `[-1,(-pi)/(4)]uu[(pi)/(4),1]`

Answer

C

Explanation

`(sin x + cos^(-1)x)-(cos x - sin^(-1)x)ge (pi)/(2)`
`therefore sin x - cos x +(pi)/(2)ge (pi)/(2)`
or `sin x - cos x ge 0`
or `sin x ge cos x`
Clearly domain of inequality is `x in [-1,1]`
`therefore x in [(pi)/(4),1]`