What Values Make f(23,x) Equal to f(33,x) for 100<x<200 Degrees?

[newchie]

Homework Statement

consider the function
f(n,x) = (sinx+sin2x+sin3x +...+sin(n-1)x+sinnx)/)cosx+cos2x+cos3x+...+cos(n-1)x+cosnx)
Find the sum of all values for which f(23,x) = f(33,x)where x is measured in degrees from 100<x<200

Homework Equations

you get obviously tanx+tan2x...
not sure where to go other than pluggin in values

The Attempt at a Solution

Plugging in values, testing cases trying different methods including demoivres, but doesent help. Help is appreciated!

 

[SammyS]

Homework Statement

consider the function
f(n,x) = (sinx+sin2x+sin3x +...+sin(n-1)x+sinnx)/(cosx+cos2x+cos3x+...+cos(n-1)x+cosnx)
Find the sum of all values for which f(23,x) = f(33,x)where x is measured in degrees from 100<x<200

Homework Equations

you get obviously tanx+tan2x...
not sure where to go other than pluggin in values

The Attempt at a Solution

Plugging in values, testing cases trying different methods including demoivres, but doesent help. Help is appreciated!

You do not get tan(x)+tan(2x)+ ...

\displaystyle \frac{a+b+c}{e+f+g}\ne\frac{a}{e}+\frac{b}{f}+ \frac{c}{g}\ \ \

 

[newchie]

You do not get tan(x)+tan(2x)+ ...

\displaystyle \frac{a+b+c}{e+f+g}\ne\frac{a}{e}+\frac{b}{f}+ \frac{c}{g}\ \ \

ah yes woops, i misread hehe, anyways do you have an approach on this problem