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The soluation set of inequality (sinx+co...

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

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]`

Text Solution

Verified by Experts

The correct Answer is:
C
`(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]`
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