Question 1081080
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<pre>
If tan(x) + cot(x) = 2, then 

   {{{sin(x)/cos(x)}}} + {{{cos(x)/sin(x)}}} = 2,  ---->

   {{{sin^2(x)/(sin(x)*cos(x))}}} + {{{cos^2(x)/(sin(x)*cos(x))}}} = 2,  ---->

   {{{(sin^2(x) + cos^2(x))/(sin(x)*cos(x))}}} = 2,  ---->

   {{{1/(sin(x)*cos(x))}}} = 2,

   2sin(x)*cos(x) = 1  --->  sin(2x) = 1  --->  2x = {{{pi/2}}}  --->  x = {{{pi/4}}}  or  x = {{{3pi/4}}}. 

   In any case, tan(x) = 1  and  cot(x) = 1.


       So, we proved that  <U>if  tan(x) + cot(x) = 2  then  tan(x) = 1  and  cot(x) = 1</U>.



2.  Having this, you have  {{{tan^17(x) + cot^17(x)}}} = {{{1^17 + 1^17}}} = 1 + 1 = 2.
</pre>

<U>Answer</U>. &nbsp;if  tan(x) + cot(x) = 2  &nbsp;then  &nbsp;{{{tan^17(x) + cot^17(x)}}} = 2.



Solved.