Hi
Dividing by makes you lose solutions.
You must factor.
leading to or
You can't divide by as it can be equal to 0.
Here is how to do.
factorise by cos(theta) :
the product ab=0 if and only if a=0 or b=0
----> or
For the first one... there are infinitely many solutions !
we know that
but since cos(-x)=cos(x), we know that
moreover, cos is a 2pi-periodic function.
Hence
these give all the possible solutions for cos(theta)=0
(in general, if a is such that cos(a)=b, then the solutions to cos(x)=b are in the form a+2kpi or -a+2kpi, for any integer k)
For the second one, there are infinitely many solutions too.
we know that
but we know that . Thus
again, sin is a 2pi-periodic function.
Hence
this can be rewritten :
Finally, the solutions are :
does it look good to you ?
Edit : woops, a bit late