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

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: (frac(sintheta)(1+costheta))=tan(theta/2)

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

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

Prove that (frac(1+sintheta)(1+costheta)) + (frac(1-sintheta)(1-costheta)) = 2(cosec^2theta-cottheta)

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

Prove the following: (frac(sin^3theta+cos^3theta)(sintheta+costheta))+(frac(sin^3theta-cos^3theta)(sintheta-costheta))=2

Show that: |(sintheta,costheta),(-costheta,sintheta)| =1

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