Question 983895
Use the identity cos^2 = 1 - sin^2 to go from this


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


to this


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


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Now combine like terms to get {{{-sin^2(x) - 3sin(x) - 2 = 0}}}


Let {{{z = sin(x)}}} which gives this new equation {{{-z^2 - 3z - 2 = 0}}}


Solve the equation {{{-z^2 - 3z - 2 = 0}}} for z, using the quadratic formula. There are 2 solutions for z and they are {{{z = -1}}} or {{{z = -2}}}


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Recall that {{{z = sin(x)}}} so saying {{{z = -1}}} or {{{z = -2}}} really means 


{{{sin(x) = -1}}} or {{{sin(x) = -2}}}


I'll let you solve from here. Use the unit circle. Hint: one of those equations has no solution.