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sectheta+tantheta=tan(pi/4+theta/2)...

`sectheta+tantheta=tan(pi/4+theta/2)`

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Prove that: (sectheta-tantheta)/(sectheta+tantheta)=1-2sectheta.tantheta+2tan^(2)theta

Prove that: sqrt((1-sintheta)/(1+sintheta)) ={sectheta-tantheta} ,if -pi/2 = -sectheta+tantheta , if pi/2 < theta < (3pi)/2

The locus of the point (sectheta+tantheta,sectheta-tantheta) where theta is parameter, is

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