How do you prove #csc^-1(x)=pi/2 -sec^-1(x)#?

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How do you prove #csc^-1(x)=pi/2 -sec^-1(x)#?

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Answer 1 · 2016-05-07T14:15:47

as below

Explanation:

Let #csc^-1x=theta#
#=>x=csctheta#
#=>x=sec(pi/2-theta)#
#=>sec^-1x=sec^-1sec(pi/2-theta)#
#=>sec^-1x=(pi/2-theta)#
#=>sec^-1x=(pi/2-csc^-1x)# [putting #theta=csc^-1x#]
#=>csc^-1x=(pi/2-sec^-1x)#
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How do you prove #csc^-1(x)=pi/2 -sec^-1(x)#?

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