If cos A = 4/5 , then the value of tan A is

(A) 3/5  (B) 3/4    (C) 4/3  (D) 5/3

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Question 4 If cos A = 4/5 , then the value of tan A is (A) 3/5 (B) 3/4 (C) 4/3 (D) 5/3 Since cos A = 4/5 ∴ sec A = 𝟓/𝟒 Now, 1 + tan2 A = sec2 A Putting values 1 + tan2 A = (5/4)^2 1 + tan2 A = 25/16 tan2 A = 25/16−1 tan2 A = (25 − 16)/16 tan2 A = 9/16 tan2 A = (𝟑/𝟒)^𝟐 Removing square tan A = ± 3/4 Since only positive values are given in options tan A = 𝟑/𝟒 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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.