2sinx*cosx+cosx=0 why we can not divide with cosx

2sinx*cosx+cosx=0

cosx(2sinx+1)=0       why we can not divide with cosx
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cos(x) can be zero, and it’s not possible to divide by zero. So cos(x)=0 is a solution, and any odd multiple of 90° or π/2 has a cosine of 0. The other solution is given by sin(x)=-½, and x=-30° (-π/6), or 330° (11π/6) or 210° (7π/6).

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