Question 1181371
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(cos(x) + sin(x) )*(1-2sin(x))=0
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<pre>
This basic equation deploys in two independent equations.


First equation is

    cos(x) + sin(x) = 0.


It is equivalent to 

    cos(x) = -sin(x)

    tan(x) = -1


Its general solution is

    x = {{{arcsin(-1) + k*pi}}} = {{{-pi/4 + k*pi}}}.     (1)



Second equation is 

    1 - 2sin(x) = 0,

which is the same as

    sin(x) = {{{1/2}}}.


Its general solution is

    x = {{{pi/6 + 2k*pi}}}  and  x = {{{5pi/6 + 2k*pi}}}.    (2)



<U>ANSWER</U>.  The general solution of the given equation is the union of these sets (1) and (2)

         x = {{{-pi/4 + k*pi}}}  and  x = {{{pi/6 + 2k*pi}}},  x = {{{5pi/6 + 2k*pi}}}.
</pre>

Solved.