Which one of the following in not correct ?

Options

A. `sin^(-1){sin(5 pi//4)}=-pi//4`
B. `sec^(-1){sec(5 pi//4)}=3pi//4`
C. `tan^(-1){tan(5pi//4)}=pi//4`
D. `cosec^(-1){cosec(7 pi//4)}=pi//4`

Answer

D

Explanation

Option (a)
`sin^(-1)("sin"(5pi)/(4))=(-pi)/(4)`
`rArr "sin"(5pi)/(4)=sin((-pi)/(4))`
`rArr sin(pi+(pi)/(4))=-"sin"(pi)/(4)`
`rArr -sin((pi)/(4))=-sin((pi)/(4))`
Hence it is correct.
Option (b)
`sec^(-1)("sec"(5pi)/(4))=(3pi)/(4)`
`rArr "sec"(5pi)/(4)="sec"(3pi)/(4)`
`rArr sec(2pi-(3pi)/(4))="sec"(3pi)/(4)`
`rArr "sec"(3pi)/(4)= "sec"(3pi)/(4)`
Hence, it is correct
Option (c)
`tan^(-1)("tan"(5pi)/(4))=(pi)/(4)`
`rArr "tan"(5pi)/(4)="tan"(pi)/(4)`
`rArr tan(pi+(pi)/(4))="tan"(pi)/(4)`
`rArr "tan"(pi)/(4)="tan"(pi)/(4)`
Hence it is correct
Option (d)
`"cosec"^(-1)("cosec"(7pi)/(4))=(pi)/(4)`
`rArr "cosec"(7pi)/(4)="cosec"(pi)/(4)`
`rArr "cosec"(2pi-(pi)/(4))="cosec"(pi)/(4)`
`rArr "-cosec"(pi)/(4)="cosec"(pi)/(4)`
Hence it is not correct.