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

(A) 0   (B) 1   (C) 2   (D)

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  1. Chapter 8 Class 10 Introduction to Trignometry (Term 1)
  2. Serial order wise

Transcript

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 89° Using tan θ = cot (90° − θ) = tan 1° tan 2° tan 3° … tan 44° tan 45° cot (90° − 46°) … cot (90° − 89°) = tan 1° tan 2° tan 3° … tan 44° tan 45° cot 44° … cot 1° = tan 1° cot 1° tan 2° cot 2° … tan 44° cot 44° × tan 45° = tan 1° × 𝟏/(𝒕𝒂𝒏 𝟏°) . tan 2° × 𝟏/(𝒕𝒂𝒏 𝟐°) … 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
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.