Answer :

We can write,


tan = tan (2π – )


tan(2π – θ )


= tan(–θ)


= –tanθ


tan becomes –tan


–tan = –


2tan = –


The question converts to cosec–1(–)


Let cosec–1 = y


cosec y =


= cosec


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


and cosec


Therefore, the principal value of cosec–1 is .


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