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#1 Posted 10:23am 24-01-10 number of solutionsNumber os solutions of the eqn tan x+ sec x= 2cos x , lying in the interval [0,2∩) is a) 0 b)1 c)2 d)3 |
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#2 Posted 10:45am 24-01-10 Re: number of solutionstanx+secx= 2cosx multiply by cosx sinx+ 1 = 2cos[p]2[/p]x sinx+1 = 2- 2sin[p]2[/p]x 2sin[p]2[/p]x+ sinx - 1 = 0 2sin[p]2[/p]x + 2sinx - sinx - 1 = 0 2sinx(sinx+1) - (sinx+1) = 0 (sinx+1)(2sinx-1) = 0 sinx= -1 , sinx = 1/2 so x = 3pie/2 , or x = pie/6 ,or x =pie - pie/6 but for x = 3pie/2 , tanx isnt defined hence x = pie/6 or 5pie/6 hence 2 solutions is the ans correct ? [hide] y m i not able to open latex ?[/hide]
me : giv me some more time , giv me sum brain , giv me another chance , to write my paper once again ,
examiner : na na na na , na na na na , na na na na na na na na na na !!! Edited on 10:48am 24-01-10 |
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#3 Posted 11:02am 24-01-10 Re: number of solutionsGood work btw for the number of solutions, you could also have looked at sinx+ 1 = 2cos[p]2[/p]x sin x = cos (2x) and from graph tried to conclude the same!
-when spring comes, it melts the snow one flake at a time… |
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#4 Posted 11:09am 24-01-10 Re: number of solutionsyes sir , i do want to improve my graphing abilities , and m learning the same from Tiit !!! and some frndz wich i made here !!! [1]
me : giv me some more time , giv me sum brain , giv me another chance , to write my paper once again ,
examiner : na na na na , na na na na , na na na na na na na na na na !!! |
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#5 Posted 0:57pm 24-01-10 Re: number of solutionsNishant sir , plz show the graphical soln. |
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#6 Posted 1:28pm 24-01-10 Re: number of solutionsok....i hav to say something [3] will teh no of point of intersection of grphs sin x and cos (2x) give the no of solns of tan x+ sec x= 2cos x bec no of point of intersection of grphs sin x and cos (2x) will be 3......3pi/2 will also be its soln but for this tan x+ sec x= 2cos x 3pi/2 is not a soln.....bec tan(3pi/2) is not defined 
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#7 Posted 2:24pm 24-01-10 Re: number of solutionsOUT OF THESE , one point of intersection is not the solution [image]39823115.jpg[/image]
me : giv me some more time , giv me sum brain , giv me another chance , to write my paper once again ,
examiner : na na na na , na na na na , na na na na na na na na na na !!! |
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#8 Posted 2:57pm 24-01-10 Re: number of solutionsu r rong i guess qwerty sin 270=-1 cos(2*270)=-1 so how can u say 3pi/2 is not a soln of sinx=cos2x
Edited on 3:01pm 24-01-10 |
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#9 Posted 07:16am 25-01-10 Re: number of solutionsbhai tanx ka kya ??? [5]
me : giv me some more time , giv me sum brain , giv me another chance , to write my paper once again ,
examiner : na na na na , na na na na , na na na na na na na na na na !!! |
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#10 Posted 07:44am 25-01-10 Re: number of solutionsAnother way: [im]http://codecogs.izyba.com/gif.latex?%5Ctan%20x%20+%20%5Csec%20x%20%3D%202%20%5Ccos%20x%20%5CRightarrow%20%5Csec%20x%20-%20%5Ctan%20x%20%3D%20%5Cfrac%7B1%7D%7B2%20%5Ccos%20x%7D%20%3D%20%5Cfrac%7B%5Csec%20x%7D%7B2%7D[/im] [im]http://codecogs.izyba.com/gif.latex?%5CRightarrow%20%5Csec%20x%20%3D%202%20%5Ctan%20x[/im] From the 1st eqn this implies [im]http://codecogs.izyba.com/gif.latex?%5Ccos%20x%20%3D%20%5Cpm%20%5Cfrac%7B%5Csqrt%203%7D%7B2%7D[/im] and cos and tan must both have the same sign. So 2 solutions |
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