Question 1208912
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Solve for x.
2sinx + 2tanx = 0
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You want to solve

    2sin(x) + 2tan(x) = 0.


The domain of this equation are all real numbers except of  x = {{{pi/2+k*pi}}},  where cos(x) = 0.


Rewrite in the form

    2sin(x) + {{{2*(sin(x)/cos(x))}}} = 0.


In the domain, multiply both sides by  {{{cos(x)/2}}}.


Since  cos(x) =/= 0,  you will get an equivalent equation

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


Factor

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


So, either sin(x) = 0,  giving the solutions  x = {{{k*pi}}},  k = 0, +/-1, +/-2, . . .          (1)

    or  cos(x) + 1 = 0,  cos(x) = -1,  giving  x = {{{pi + 2k*pi}}},  k = 0, +/-1, +/-2, . . .    (2)



The set (2) is part of set (1) - so, the general solution to the given equation is the set

    x = {{{k*pi}}},  k = 0, +/-1, +/-2, . . .


<U>ANSWER</U>.  The general solution to the given equation is the set  x = {{{k*pi}}},  k = 0, +/-1, +/-2, . . .
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Solved.