Question 1175310
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Treat each equation as an equation in which the variable(s) is/are trig functions.  Solve by regular algebraic methods; then use your unit circle.<br>
I'll just get you started on each one; you won't learn anything from this if I do all the work for you.<br>
1.  5cosx + Square root 3 = 3cosx
This is a linear equation in cosx.  Solve by getting the variable on one side and the number on the other:
2cosx = -sqrt(3)
...<br>
2.  3(tanx)^2 - 1 = 0
This is a quadratic equation in tanx.  It is also in the form of a difference of squares.  Factor it that way.
(sqrt(3)tanx+1)(sqrt(3)tanx-1) = 0
tanx = -1/sqrt(3)  or  tanx = 1/sqrt(3)
...<br>
3.  2(cosx)^2 - cosx = 1
This is quadratic in cosx; get everything on one side and factor.
2(cosx)^2-cosx-1 = 0
(2cosx+1)(cosx-1) = 0
...<br>
4.  4(sinx)^3 + 2(sinx)^2 - 2sinx - 1 = 0
A cubic in sinx; 4 terms, so factor by grouping.
(2(sinx)^2)(2sinx+1)-(2sinx+1) = 0
{2(sinx)^2-1)(2sinx+1) = 0
...<br>
5.2sinxcosx - sinx = 0
This is quadratic in both sinx and cosx.  Factor out the factor common to both terms.
(sinx)(2cosx-1) = 0
...<br>