Question 1113281
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{{{cosx + sqrt (3sinx) = -1}}}<br>
{{{sqrt(3sinx) = -1-cosx}}}<br>
The left hand side is a square root, so it has to be 0 or positive.<br>
The range of cosx is from -1 to 1; that means the range of the right hand side is from -2 to 0.<br>
The right hand side is must be 0; that means cosx has to be -1.<br>
sinx is 0 (and so sqrt(3sinx) is 0) when cosx is -1; so the equation is satisfied whenever cosx is -1, and ONLY then.<br>
In the interval 0 to 2pi, the only solution is x=pi.<br>
The complete solution is x = pi plus any (positive or negative) multiple of 2pi.