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

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

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

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

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

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

Prove the following identities: (1+cottheta-cosectheta)(1+tantheta+sectheta)=2

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

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

Prove the following identities: (sec theta-tan theta+1)/(sec theta+tantheta+1)=(1-sin theta)/(cos theta)

Prove the following identities: sqrt(sec^2theta+cos e c^2theta)=tantheta+cottheta