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

Question

1513 views around the world

You can reuse this answer
Creative Commons License

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

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

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