Question 9 - NCERT Exemplar - MCQ - Chapter 8 Class 10 Introduction to Trignometry

Last updated at Dec. 16, 2024 by

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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo