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If 5 tan β = 4, the 5 sin⁡β - 2 cos⁡β/5 sin⁡β - 2 cos⁡β  =

(a) 1/3   (b) 2/5   (c) 3/5   (d) 6

 

This question is Similar to Question 15 - NCERT Exemplar - MCQ

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Question 18 If 5 tan Ξ² = 4, the (5 sin⁑〖𝛽 γ€—βˆ’ 2 cos⁑𝛽)/(5 sin⁑〖𝛽 γ€—+ 2 cos⁑𝛽 ) = (a) 1/3 (b) 2/5 (c) 3/5 (d) 6 Given 5 tan 𝛽 = 4 tan 𝛽 = πŸ’/πŸ“ Now, (5 sin⁑〖𝛽 γ€—βˆ’ 2 cos⁑𝛽)/(5 sin⁑〖𝛽 γ€—+ 2 cos⁑𝛽 ) Dividing numerator and denominator by cos 𝛽 = (5 sin⁑𝛽/cos⁑𝛽 βˆ’ 2 co𝑠⁑𝛽/cos⁑𝛽 )/(5 sin⁑𝛽/cos⁑𝛽 + 2 co𝑠⁑𝛽/cos⁑𝛽 ) = (πŸ“ π­πšπ§β‘γ€–π›½ βˆ’ πŸγ€—)/(πŸ“ π­πšπ§β‘γ€–π›½ + πŸγ€— ) Putting tan ΞΈ = πŸ’/πŸ“ = (5 Γ— 4/5 βˆ’ 2)/(5 Γ— 4/5 + 2) = (4 βˆ’ 2)/(4 + 2) = 2/6 = 𝟏/πŸ‘ So, the correct answer is (a)

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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.