If tan⁑A=3/4 , find the value of 1/sin⁑A +1/cos⁑A

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

Transcript

Question 25 (Choice - 1) If tan⁑𝐴=3/4 , find the value of 1/sin⁑𝐴 +1/cos⁑𝐴 Given, tan A = 3/4 (𝑆𝑖𝑑𝑒 π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’ π‘‘π‘œ π‘Žπ‘›π‘”π‘™π‘’ 𝐴)/(𝑆𝑖𝑑𝑒 π‘Žπ‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘ π‘‘π‘œ π‘Žπ‘›π‘”π‘™π‘’ 𝐴) = 3/4 𝐡𝐢/𝐴𝐡 = 3/4 Let BC = 3x & AB = 3x We find AC using Pythagoras Theorem In right triangle ABC Using Pythagoras theorem (AC)2 = (BC)2 + (AB)2 (AC)2 = (3x)2 + (4x)2 (AC)2 = 9x2 + 16x2 (AC)2 = 25x2 AC = √25π‘₯2 AC = 5x Now, sin A = (𝑆𝑖𝑑𝑒 π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’ π‘‘π‘œ π‘Žπ‘›π‘”π‘™π‘’ 𝐴)/π»π‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’ sin A = 𝐡𝐢/𝐴𝐢 sin A = 3π‘₯/5π‘₯ sin A = πŸ‘/πŸ“ cos A = (𝑆𝑖𝑑𝑒 π‘Žπ‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘ π‘‘π‘œ 𝐴)/π»π‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’ cos A = 𝐴𝐡/𝐴𝐢 cos A = 4π‘₯/5π‘₯ cos A = πŸ’/πŸ“ Now, 1/sin⁑𝐴 +1/cos⁑𝐴 = 1/(3/5)+1/(4/5) = 5/3+5/4 = (5 Γ— 4 + 5 Γ— 3)/(3 Γ— 4) = (20 + 15)/12 = πŸ‘πŸ“/𝟏𝟐

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.