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Prove that [1 + cot α - sec(α + (π/2))][1 + cot α + sec(α + (π/2))] = 2cot α |
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Answer» sec(α + π/2) = - cosec α LHS = [(1 + cot α) + cosec α][(1 + cot α) – cosec α] = (1 + cot α)2 – cosec2 α = 1 + cot2 α + 2 cot α – cosec2 α [∵ 1 + cot2 α = cosec2 α] = cosec2 α + 2 cot α – cosec2 α = 2 cot α = RHS |
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