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Prove each of the following identities : `(i) 1+ (cot^(2) theta)/((1+ "cosec"theta))= "cosec" theta ` ` (ii) 1+ (tan^(2) theta)/((1+ sec theta))= sec

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Prove each of the following identities :
`(i) 1+ (cot^(2) theta)/((1+ "cosec"theta))= "cosec" theta `
` (ii) 1+ (tan^(2) theta)/((1+ sec theta))= sec theta `
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(i) Write `cot^(2)theta=("cosec"^(2)theta -1).`
(ii) Write `tan^(2)theta=(sec^(2)theta-1).`
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