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| 1. |
If cosecA-cotA=4/5, then prove that cosecA=41/40. |
| Answer» (cosecA - cotA)^2={4/5}^2, cosecA^2 +cotA^2 - 2coseccot= 16/25, 1+cotA^2 +cotA^2 - 2cosA/sinA^2 = 16/25, 1 + (2cos^A - 2cosA)/sin^2A = 16/25, 1 +{-2cosA(-cosA +1)}/sin^2A = 16/25, 1+{-2cosA(1- cosA)}/(1-cosA)(1+cosA), 1+{-2cosA}/(1+cosA)=16/25, (1+cosA-2cosA)/(1+cosA)=16/25, (1-cosA)/(1+cosA)=16/25, on cross multiplying rhs and Lsh,( 25 -25cosA = 16 +16cosA),( 9 = 41cosA),( cosA =9/41),(cos= adj side/hypot),(So, here using Pythagoras theorem we get perpendicular=40,hypotenuse=41& base= 9),cosecA=hypot/perpendicular, (cosecA = 41/40) hence proved It take long time to solve it on mobile by using keypad so please do likes ? | |