I'm getting an incorrect solution when solving:
a Cos[x]^2 + b Sin[x]^2 + c Sin[x] Cos[x] == 0
for x. Any ideas on what's going on?
Here's what I'm doing:
f[x_] := a Cos[x]^2 + b Sin[x]^2 + c Sin[x] Cos[x]
FullSimplify[Solve[f[x] == 0, x]]
FullSimplify[f[ (copy and paste solution from output above) ]]
The output of this last expression is not 0!