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The value of sec(sin^-1(sin((-50pi)/9))+...

The value of `sec(sin^-1(sin((-50pi)/9))+cos^-1(cos((31pi)/9)))`

A

`"sec"(10pi)/(9)`

B

`"sec"(pi)/(9)`

C

`1`

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
D
`sin^(-1)(-sin.(50pi)/(9))=sin^(-1)(sin(-6pi+(4pi)/(9)))`
`=sin^(-1)(sin.(4pi)/(9))`
`=(4pi)/(9)`
`cos^(-1)cos(-(31pi)/(9))=cos^(-1)cos((31pi)/(9))`
`=cos^(-1)cos(4pi-(5pi)/(9))=cos^(-1)cos.(5pi)/(9)=(5pi)/(9)`
Hence, given equals to sec `((4pi)/(9)+(5pi)/(9))=sec pi =-1`.
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