tan^2+ cot^2+ 2 = sec0 . cosec 0
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tan²x + cot²x +2 = secx.cosecx
LHS
tan²x + cot²x + 2
sin²x/cos²x + cos²/sin²x + 2
sin⁴x + cos⁴x + 2sin²xcos²x/sin²xcos²x
(sin²x+cos²x)²/sin²xcos²x
1/sin²xcos²x
sec²x.cosec²x
Hence proved
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