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tanA=sinA/cosA

cotA=cosA/sinA

therefore

using the identity cosec^2A-cot^2A=1

we get cosec^2A=1+cot^2a

1/sin^2A=1+cot^2A

sin^2A=1/1+cot^2A

using identity sec^2A-tan^2A=1

we get

sec^2A=1+tan^2A

sec^2A=1+1/cot^2A

sec^2A=cot^2A+1/cot^2A