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)))

 

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)