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

Prove the following : sec^2 theta + cosec^2 theta = sec^2 theta times cosec^ theta

(1 - cos^(2)theta)cot^(2)theta

Prove the following: 2sec^2theta-sec^4theta-2cosec^2theta+cosec^4theta=cot^4theta-tan^4theta

Prove the following : cot^2 theta - tan^2 theta = cosec^2 theta -sec^2 theta

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

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

Prove the following: 2(sin^6theta+cos^6theta)-3(sin^4theta+cos^4theta)+1=0

Prove the following: (frac(1-cos2theta)(1+cos2theta))=tan^2theta

Prove that : sec^(2)theta+"cosec"^(2)theta=sec^(2)theta*"cosec" ^(2)theta