Finding epsilon satisfy a trigonometric function.

I need to find the value of epsilon (e) that satisfy the function cot(e)^2*cot(2*e)^2 == sin(2*e)^2 where pi/4<e<pi/2

Answer 1

[sawsan]

Thanks a lot. I found the solution. I share it here if someone want to use it.

syms x
f = cot(x).^2*cot(2*x).^2 - sin(2*x).^2;
 vpasolve(f,[pi/3 pi/2])

ans =

1.326722925756775867399902790294

[Star Strider]

There are 4 solutions on the interval (-pi/2,pi/2).

[Sawsan Alhowaity]

yes, but on the interval [pi/3, pi/2] there is only one solution. Thanks for replying.

[Star Strider]

Your original Question asked for all solutions on the interval -pi/2 to pi/2.

Answer 2

[KSSV]

clc; clear all ;
syms e
eqn = cot(e)^2*cot(2*e)^2 == sin(2*e)^2 ;
[solx, params, conds] = solve(eqn, e, 'ReturnConditions', true) ;

Answer 3

[Star Strider]

Another approach:

trig_e = @(e) cot(e).^2*cot(2*e).^2 - sin(2*e).^2;
v = linspace(-pi/2, pi/2, 4);
for k1 = 1:length(v)
    e(k1) = fzero(trig_e, v(k1));
end

e =
    -1.3267e+000  -541.3248e-003   541.3248e-003     1.3267e+000