Question 1045173
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Find all values of x in the interval [0, 2π] that satisfy the equation 
6 cos(x) + 3 sin(2x) = 0 
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<pre>
6*cos(x) + 3*sin(2x) = 0,

Divide both sides by 3 and replace  sin(2x)  by  2*sin(x)*cos(x):  sin(2x) = 2*sin(x)*cos(x).  You will get

2*cos(x) + 2*sin(x)*cos(x) = 0.

Divide both sides by 2. You will get

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

Factorize: 

cos(x)*(1+sin(x)) = 0.

The equation deploys in two independent equations:


1)  cos(x) = 0  --->  x = {{{pi/2}}}  and/or  x = {{{3pi/2}}}.


2)  1+sin(x) = 0  --->  sin(x) = -1  --->  x = {{{pi}}}.

<U>Answer</U>. The solutions are {{{pi/2},  {{{pi}}}  and {{{3pi/2}}}.
</pre>