(i) tan^2A + cot^2A + 2 = sec^2A cosec^2A. prove
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L.H.S.
=> tan² A + cot² A + 2
=> sin² A/cos² A + cos² A/sin² A + 2
=> (sin⁴A + cos⁴A + 2 sin²A.cos²A)/ (sin²A.cos²A)
=> (sin² A+ cos² A)²/(sin²A.cos²A)
=> (1)²/(sin²A.cos²A) [ sin²A + cos²A = 1]
=> 1/sin²A . 1/cos²A
=> cosec²A . sec²A
=> sec²A . cosec²A = R.H.S.
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