If 4 tan β = 3, then (4 sin⁡β  - 3 cos⁡β)/(4 sin⁡β  + 3 cos⁡β ) =

(a) 0  (b) 1/3      (c) 2/3        (d) 3/4 

 

This question is inspired from Question 15 - NCERT Exemplar - MCQ - Chapter 8 Class 10 - Introduction to Trignometry

 

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Question 18 If 4 tan β = 3, then (4 sin⁡𝛽 − 3 cos⁡𝛽)/(4 sin⁡𝛽 + 3 cos⁡𝛽 ) = (a) 0 (b) 1/3 (c) 2/3 (d) 3/4 Given 4 tan β = 3 tan β = 𝟑/𝟒 Now, (4 sin⁡〖𝛽 − 3 cos⁡𝛽 〗)/(4 sin⁡〖𝛽 + 〖3 cos〗⁡𝛽 〗 ) Dividing numerator and denominator by cos θ = (4 sin⁡𝛽/cos⁡𝛽 − 3 cos⁡𝛽/cos⁡𝛽 )/(4 sin⁡𝛽/cos⁡𝛽 + 3 cos⁡𝛽/cos⁡𝛽 ) = (𝟒 𝐭𝐚𝐧⁡〖𝛽 − 𝟑〗)/(𝟒 𝐭𝐚𝐧⁡〖𝜽 + 𝟑〗 ) Putting tan 𝛽 = 𝟑/𝟒 = (4 × 3/4 − 3)/(4 × 3/4 + 3) = (3 − 3)/(3 + 3) = 0/6 = 0 So, the correct answer is (a)

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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.