How do you verify the identity #sqrt((sectheta-1)/(sectheta+1))=abs((sectheta-1)/tantheta)#?

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Answer 1 · 2016-09-02T18:15:48

See below.

#sqrt((sectheta-1)/(sectheta+1))=abs((sectheta-1)/tantheta)#

squaring both sides

#(sectheta-1)/(sectheta+1)=((sectheta-1)/tantheta)^2#

or

#1/(sectheta+1)=(sectheta-1)/tan^2theta#

and finally

#tan^2theta = sec^2theta - 1#