Question 1042969
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2cos^2x-3sinx-3=0
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<pre>
{{{2cos^2(x) - 3sin(x) - 3}}} = {{{0}}}.

Substitute  {{{cos^2(x)}}} = {{{1 - sin^2(x)}}}  to get the equation uniform for sin(x). You will get

{{{2*(1-sin^2(x)) - 3sin(x) -3}}} = {{{0}}},  --->

{{{2-2sin^2(x) - 3sin(x) - 3}}} = {{{0}}},

{{{2sin^2(x) + 3sin(x) +1}}} = {{{0}}}.

Factor left side

(2sin(x)+1)*(sin(x)+1) = 0.

Then the equation deploys in two separate/independent equations:

1)  2sin(x) + 1 = 0  --->  sin(x) = {{{-1/2}}}  --->  x = {{{5pi/4}}}  and/or  x = {{{7pi/4}}}.

2)  sin(x) = -1  --->  x = {{{3pi/2}}}.

<U>Answer</U>.  x = {{{5pi/4}}}  and/or  x = {{{7pi/4}}}  and/or  x = {{{3pi/2}}}.
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