Need help solving equation in terms of a variable

I think this should be a simple solution, but I have an equation set equal to zero with two variables, "L" and "k." I'd like to solve the equation for "k" or ideally for "(k*L)/2." But am having trouble using the linsolve function. Below is the equation as well as the two linsolve approaches I've tried, both of which return a division by zero error.

eq8 = cos((L*k)/2)*cos((2^(1/2)*L*k)/4) - (2^(1/2)*sin((L*k)/2)*sin((2^(1/2)*L*k)/4))/2 == 0

%linsolve(eq8, k)

%linsolve(eq8, (k*L)/2)

Answer 1

[Walter Roberson]

syms L k Lk2
eq8 = cos((L*k)/2)*cos((2^(1/2)*L*k)/4) - (2^(1/2)*sin((L*k)/2)*sin((2^(1/2)*L*k)/4))/2 == 0

eq8 = 

K = solve(k*L/2 == Lk2, k)

K = 

eq8kL = subs(eq8, k, K)

eq8kL = 

vpasolve(eq8kL)

ans = 

fplot(lhs(eq8kL)-rhs(eq8kL), [-25 25])

Not a linear system; it is a periodic or quasi-periodic system, with an infinite number of solutions.

char(eq8kL)

ans = 'cos((2^(1/2)*Lk2)/2)*cos(Lk2) - (2^(1/2)*sin((2^(1/2)*Lk2)/2)*sin(Lk2))/2 == 0'

[Walter Roberson]

Maple says that the solutions are the θ such that

which looks reasonable from eq8kL .

Unfortunately that does not help find explicit formulas.