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

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

(sintheta+sin 2theta)/(1+costheta+cos2theta)=

Prove the following: (sintheta+cosectheta)^2+(costheta+sectheta)^2=Tan^2theta+cot^2theta+7

Prove the following identities: 1+3cosec^2thetacot^2theta+cot^6theta=cosec^6theta

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

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: (frac(1+cottheta+cosectheta)(1-cottheta-cosectheta))=(frac(cosectheta+cottheta-1)(cottheta-cosectheta+1))

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

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