If tanβ‘A=3/4 , find the value of 1/sinβ‘A +1/cosβ‘A
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CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard
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CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard
Last updated at May 29, 2023 by Teachoo
Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Question 25 (Choice - 1) If tanβ‘π΄=3/4 , find the value of 1/sinβ‘π΄ +1/cosβ‘π΄ Given, tan A = 3/4 (ππππ πππππ ππ‘π π‘π πππππ π΄)/(ππππ ππππππππ‘ π‘π πππππ π΄) = 3/4 π΅πΆ/π΄π΅ = 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 = β25π₯2 AC = 5x Now, sin A = (ππππ πππππ ππ‘π π‘π πππππ π΄)/π»π¦πππ‘πππ’π π sin A = π΅πΆ/π΄πΆ sin A = 3π₯/5π₯ sin A = π/π cos A = (ππππ ππππππππ‘ π‘π π΄)/π»π¦πππ‘πππ’π π cos A = π΄π΅/π΄πΆ cos A = 4π₯/5π₯ cos A = π/π Now, π/πππβ‘π¨ +π/πππβ‘π¨ = 1/(3/5)+1/(4/5) = 5/3+5/4 = (5 Γ 4 + 5 Γ 3)/(3 Γ 4) = (20 + 15)/12 = ππ/ππ