Question 15 - NCERT Exemplar - MCQ - Chapter 8 Class 10 Introduction to Trignometry

Last updated at April 16, 2024 by

If 4 tan θ = 3, then ((4 sin⁡ θ - cos⁡ θ)/(4 sin⁡ θ + cos⁡ θ)) is equal to

(A) 2/3   (B) 1/3    (C) 1/2  (C) 3/4

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Question 15 If 4 tan θ = 3, then ((4 sin⁡〖𝜃 − cos⁡𝜃 〗)/(4 sin⁡〖𝜃 + cos⁡𝜃 〗 )) is equal to (A) 2/3 (B) 1/3 (C) 1/2 (C) 3/4 Given 4 tan θ = 3 tan θ = 𝟑/𝟒 Now, (4 sin⁡〖𝜃 − cos⁡𝜃 〗)/(4 sin⁡〖𝜃 + cos⁡𝜃 〗 ) Dividing numerator and denominator by cos θ = (4 sin⁡𝜃/cos⁡𝜃 − co𝑠⁡𝜃/cos⁡𝜃 )/(4 sin⁡𝜃/cos⁡𝜃 + co𝑠⁡𝜃/cos⁡𝜃 ) = (𝟒 𝐭𝐚𝐧⁡〖𝜽 − 𝟏〗)/(𝟒 𝐭𝐚𝐧⁡〖𝜽 + 𝟏〗 ) Putting tan θ = 𝟑/𝟒 = (4 × 3/4 − 1)/(4 × 3/4 + 1) = (3 − 1)/(3 + 1) = 2/4 = 𝟏/𝟐 So, the correct answer is (C)

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