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
NCERT Exemplar - MCQ
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NCERT Exemplar - MCQ
Last updated at April 16, 2024 by Teachoo
Question 15 If 4 tan θ = 3, then ((4 sin〖𝜃 − cos𝜃 〗)/(4 sin〖𝜃 + cos𝜃 〗 )) 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 − cos𝜃 〗)/(4 sin〖𝜃 + cos𝜃 〗 ) Dividing numerator and denominator by cos θ = (4 sin𝜃/cos𝜃 − co𝑠𝜃/cos𝜃 )/(4 sin𝜃/cos𝜃 + co𝑠𝜃/cos𝜃 ) = (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)