Answer :

Let,


Sin–1 = y


sin y =


–sin y =


–sin


As we know sin(–θ) = –sinθ


–sin = sin


The range of principal value of sin–1 is and sin


Therefore, the principal value of Sin–1 is ….(1)


Let,


cosec–1 = z


cosec z =


–cosec z =


–cosec


As we know cosec(–θ) = –cosecθ


–cosec = cosec


The range of principal value of cosec–1 is is –{0} and


cosec


Therefore, the principal value of cosec–1 is ….(2)


From (1) and (2) we get



=


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