How to solve an equation equal to zero?

Hello,

I want to solve this equation equal to zero to find the theta, But it doesn't give me an answer there is an error. How to do it, thanks for the help.

eqn=sind(45)*sind(45+thtea)+sind(45+thtea)*sind(45+thtea)+cosd(45)*cos(45+thtea)+cosd(45+thtea)*cosd(45+thtea)==0


eqn=sind(45)*sind(45+thtea)+sind(45+thtea)*sind(45+thtea)+cosd(45)*cos(45+thtea)+cosd(45+thtea)*cosd(45+thtea)

solve(eqn,thtea)

Answer 1

[Walter Roberson]

There are at least 84 solutions, possibly more. Are you expecting to get a closed form solution that lists each of the angles that satisfies the equation? Because that is not going to happen -- trig equations seldom have closed form solutions.

Notice that your cos^2 and sin^2 add up to 1.

And notice that you have cos(45+thtea) instead of cosd(45+thtea) at one point.

syms thtea real
eqn=sind(45)*sind(45+thtea)+sind(45+thtea)*sind(45+thtea)+cosd(45)*cos(45+thtea)+cosd(45+thtea)*cosd(45+thtea)==0

eqn = 

simplify(eqn)

ans = 

solve(eqn)

Warning: Unable to solve symbolically. Returning a numeric solution using vpasolve.

ans = 

vpasolve(eqn)

ans = 

fplot([lhs(eqn)-rhs(eqn),0], [-360, 360])

fplot([lhs(eqn)-rhs(eqn),0], [-225, -70])

eqn2 = sind(45)*sind(45+thtea)+sind(45+thtea)*sind(45+thtea)+cosd(45)*cosd(45+thtea)+cosd(45+thtea)*cosd(45+thtea)==0

eqn2 = 

eqn2 = simplify(eqn2)

eqn2 = 

sol2 = solve(eqn2, 'returnconditions', true)

sol2 = struct with fields:
         thtea: 360*k + 180
    parameters: k
    conditions: in(k, 'integer')

sol2.thtea

ans = 

sol2.conditions

ans = 

[Emilia]

Ok thank you