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Discussion Response Post to: plz solve the equation

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$h0cK3r (908)

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sin(sin(sin(sinx)))=cos(cos(cos(cosx)))

we are having two functions they are

f(x)=sin(sin(sin(sinx)))

g(x)=cos(cos(cos(cosx)))

f(x) is odd and g(x) is even

we will take the function

f(x) and will try to find its maximum and minimum value

the maximum value of f(x) will be

f`(x)=cos(sin(sin(sinx)))*cos(sin(sinx))*cos(sinx)*cos x

for cos (sin x)=0

sinx should be equal to pi/2=1.54 which is not possible

hence for maxima=pi/2 +2npi

minima at -pi/2+2npi

so the maximum value of f(x)=sin(sin(sin(sin(pi/2)))

let us take the function g(x)

g`(x)=-sin(cos(cos(cosx)))*-sin(cos(cosx)))*-sin(cosx)*(-sinx)

g`(x)=sin(cos(cos(cosx)))*sin(cos(cosx)))*sin(cosx)*(sinx)

if you will double differenciate you will come to know that this function will attain maxima at x=pi/2 and its multiples

and minima at x=0,pi

now we see the maxima of f(x) and minima of g(x)

maxima of f(x)=sin(sin(sin(sin(pi/2)))=0.6784 (approx)

minima of f(x)=-0.6784 (approx)

minima of g(x)=cos(cos(cos(cos(0)))=0.6542899(approx)

maxima of g(x)=cos(cos(cos(cos(pi/2)))=0.85755321(approx)

we come to note that at the point of maximas of f(x) and g(x)

g(x) is greater

at the point of minimas of f(x) and g(x)

g(x) is greater too.

in between we dont have a extremum point otherwise we may have got a solution

hence there is no solution

i am also showing you the graph of this function

2nd year ,DCE, Electronics and Comm

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