Prove the following identities:`(cos^2A-1)(cot^2A+1)=-1`

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

Prove the following identities: (1+tan^2A)+(1+frac(1)(tan^2A))=frac(1)(Sin^2A-Sin^4A)

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

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

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

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

Prove each of the following identities : '(i) sin^(2)theta + cos^(4) theta = cos^(2) theta + sin^(4) theta (ii) "cosec"^(4) theta - "cosec"^(2) theta = cot^(4) theta + cot^(2) theta

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