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sin ^-1 ( sin θ ) > cos ^-1 ( sin θ ) ...

`sin ^-1 ( sin θ ) > cos ^-1 ( sin θ )` find the range of θ

A

`((pi)/(4), pi)`

B

`(pi, (3pi)/(2))`

C

`((pi)/(4), (3pi)/(4))`

D

`((3pi)/(4), 2pi)`

Text Solution

Verified by Experts

The correct Answer is:
C
`sin^(-1) (sin theta) gt (pi)/(2) - sin^(-1) (sin theta)`
`rArr sin^(-1) (sin theta) gt (pi)/(4)`
`rArr sin theta gt (1)/(sqrt2)`
`rArr (pi)/(4) lt theta lt (3pi)/(4)`
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