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

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

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

Prove the following identities: (frac(tan^3theta)(1+tan^2theta))+(frac(cot^3theta)(1+cot^2theta))=secthetacosectheta-2sinthetacostheta

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

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

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

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

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

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

Prove the trigonometric identities: sqrt((1-costheta)/(1+costheta))=cos e ctheta-cottheta