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Prove that - sec2 (tan-1 2) + cosec2 (cot-1 3) = 15 |
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Answer» L.H.S. = sec2(tan-1 2) + cosec2(cot-1 3) Let tan-1 2 = α tan α = 2 ∵ sec2 α = 1 + tan2 α 1 + 22 = 1 + 4 = 5 sec2 α = 5 Let again cot-1 3 = β cot β = 3 ∴ sec2 α + cosec2 β 5 + 1 + cot2 β = 5 + 1 + (3)2 = 5 + 1 + 9 = 15 = R.H.S. |
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