Question 1208914
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Solve for x.
5sec x + [tan x/cos x] = 0
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You want to solve

    {{{5/cos(x)}}} + {{{tan(x)/cos(x))}}} = 0.


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


In the domain, multiply both sides by  cos(x).


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

    5 + tan(x) = 0.

which is the same as  

    tan(x) = -5.


Hence,  x = arctan(-5) + {{{k*pi}}} = -arctan(5) + {{{k*pi}}} = -1.37340077 + {{{k*pi}}}  radians, k = 0, +/-1, +/-2, . . .


<U>ANSWER</U>.  The general solution to the given equation is the set x = -arctan(5) + {{{k*pi}}} = -1.37340077 + {{{k*pi}}}  radians, k = 0, +/-1, +/-2, . . .
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Solved.