Prove the following identities: `1/(sectheta-tantheta)=sectheta+tantheta`

Prove the following identities: (sectheta-tantheta)/(sectheta+tantheta)=1-2secthetatantheta+2tan^2theta

Prove the following identities: (frac(1-sectheta+tantheta)(1+sectheta-tantheta))=(frac(sectheta+tantheta-1)(sectheta+tantheta+1))

Prove the following identities: (1+sintheta)/(1-sintheta)=(sectheta+tantheta)^2

(sectheta+tantheta-1)(sectheta-tantheta+1)=

Prove that following identities (costheta)/(1+sintheta)=sectheta-tantheta

Prove the following identities: (1-sintheta)/(1+sintheta)= (sectheta-tantheta)^2

Prove the following identities: (cosec theta-sintheta)^2+(sectheta-costheta)^2-(tantheta-cottheta)^2=1

Prove the following identities: (cos e ctheta-sintheta)(sectheta-costheta)(tantheta+cottheta)=1

Prove the following identities : 1/( sectheta-tantheta)-1/(costheta)=1/(costheta)-1/(sectheta+tantheta)

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