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Question 25 (Choice - 1) - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at Dec. 16, 2024 by Teachoo

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

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 = 4x 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/π’”π’Šπ’β‘π‘¨ +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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo