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

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

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

Prove the following identities: (frac(cottheta)(cosectheta-1))=(frac(cosectheta+1)(cottheta))

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

Prove the following identities: (frac(sintheta)(1+costheta))+(frac(1+costheta)(sintheta))=2cosectheta

Prove the following: (frac(cosectheta+cottheta-1)(cosectheta+cottheta+1))=(frac(1-sintheta)(costheta))

Prove the following: (frac(1+cottheta+cosectheta)(1-cottheta-cosectheta))=(frac(cosectheta+cottheta-1)(cottheta-cosectheta+1))

Prove the following: (frac(1-cos2theta+sin2theta)(1+cos2theta+sin2theta))=tantheta

Prove the following identities: (sintheta+sectheta)^2+(costheta+cosectheta)^2=(1+cosecthetasectheta)^2

Prove the following: (frac(cosectheta+cottheta+1)(cottheta+cosectheta-1))=(frac(cottheta)(cosectheta-1))