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The value of (tan 1° tan 2° tan 3° ... tan 89°) is

(A) 0   (B) 1   (C) 2   (D)

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Question 9 The value of (tan 1° tan 2° tan 3° ... tan 89°) is (A) 0 (B) 1 (C) 2 (D) tan 1° tan 2° tan 3° ... tan 89° = tan 1° tan 2° tan 3° … tan 44° tan 45° tan 46° … tan 87° tan 88° tan 89° Using tan θ = cot (90° − θ) = tan 1° tan 2° tan 3° … tan 44° tan 45° cot (90° − 46°) … cot (90° − 87°) cot (90° − 88°) cot (90° − 89°) = tan 1° tan 2° tan 3° … tan 44° tan 45° cot 44° … cot 3° cot 2° cot 1° = tan 1° cot 1° tan 2° cot 2° tan 3° cot 3° … tan 44° cot 44° × tan 45° = tan 1° × 𝟏/(𝒕𝒂𝒏 𝟏°) . tan 2° × 𝟏/(𝒕𝒂𝒏 𝟐°) . tan 3° × 𝟏/(𝒕𝒂𝒏 𝟑°) … tan 44° × 𝟏/(𝒕𝒂𝒏 𝟒𝟒°) × tan 45° = 1 . 1 . 1 … 1 × tan 45° = tan 45° = 1 So, the correct answer is (B)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.