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Prove each of the following identities :...

Prove each of the following identities :
` (1+ cos theta - sin^(2) theta)/(sin theta (1+ cos theta)) = cot theta `

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Prove each of the following identities : (cos theta) /((1- tan theta)) - (sin^(2) theta)/((cos theta - sin theta)) = (cos theta + sin theta)

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Prove each of the following identities : (1+ tan theta + cot theta )( sin theta - cos theta ) =((sec theta)/("cosec"^(2) theta ) - ("cosec"theta)/(sec^(2)theta))

Prove the following identities: (cos ec theta-sin theta)(sec theta-cos theta)=(1)/(tan theta+cot theta)