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

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

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tan theta/(1-cot theta)+cot theta/(1-tan theta)=1+sec theta cosec theta