If the angles of βˆ†ABC are in ratio 1 : 1 : 2, respectively (the largest angle being angle C), then the value of  (sec A)/(cosec B)-tan⁑A/cot⁑B  is :

(a) 0   (b) 1/2  (c) 1   (d) √3  /2

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  1. Class 10
  2. Solutions of Sample Papers for Class 10 Boards

Transcript

Question 14 If the angles of βˆ†ABC are in ratio 1 : 1 : 2, respectively (the largest angle being angle C), then the value of (𝑠𝑒𝑐 𝐴)/(π‘π‘œπ‘ π‘’π‘ 𝐡)βˆ’tan⁑𝐴/cot⁑𝐡 is : (a) 0 (b) 1/2 (c) 1 (d) √3 /2 Since angles are in ratio 1 : 1 : 2 Let angles be ∠ A = x ∠ B = x ∠ C = 2x Now, In Ξ” ABC By Angle sum property ∠ A + ∠ B + ∠ C = 180Β° x + x + 2x = 180Β° 4x = 180Β° x = (180Β° )/4 x = 45Β° Thus, ∠ A = x = 45Β°, ∠ B = x = 45Β° , ∠ C = x = 90Β° Now, (𝑠𝑒𝑐 𝐴)/(π‘π‘œπ‘ π‘’π‘ 𝐡)βˆ’tan⁑𝐴/cot⁑𝐡 = (𝒔𝒆𝒄 πŸ’πŸ“Β° )/(𝒄𝒐𝒔𝒆𝒄 πŸ’πŸ“Β°)βˆ’π’•π’‚π’β‘γ€–πŸ’πŸ“Β°γ€—/π’„π’π’•β‘γ€–πŸ’πŸ“Β° γ€— = √2/√2βˆ’1/1 = 1 βˆ’ 1 = 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.