Question 1138387
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<pre>
Apply the formula for tangent of the sum of arguments


    tan(a + b) = {{{(tan(a)+tan(b))/(1-tan(a)*tan(b))}}},


which is valid for all values of "a" and "b", where the tangent function is defined.


In your case,  a = {{{3pi/4)}}},  b = {{{theta}}},  and  {{{tan(3pi/4)}}} = -1,  so


    {{{tan(3pi/4+ theta)}}} = {{{(tan(3pi/4)+tan(theta))/(1-tan(3pi/4)*tan(theta))}}} = {{{((-1)+tan(theta))/(1-(-1)*tan(theta))}}} = {{{(-1+tan(theta))/(1+tan(theta))}}} = 


        now substitute {{{tan(theta)}}} = {{{-1/2}}} to get


    {{{tan(3pi/4+ theta)}}} = {{{(-1 - (-1/2))/(1+ (-1/2))}}} = {{{((-3/2))/((1/2))}}} = -3.      <U>ANSWER</U>
</pre>

Solved.


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