Q. 3 A3.7( 3 Votes )

# For the principal

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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