tanx + cotx = 2

Found 2 solutions by MathLover1, ikleyn:

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Answer by MathLover1(20340)   (Show Source):

You can put this solution on YOUR website!

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for

or radians

we know and

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then

Answer by ikleyn(49513)   (Show Source):

You can put this solution on YOUR website!
.

If tan(x) + cot(x) = 2, then 

    +  = 2,  ---->

    +  = 2,  ---->

    = 2,  ---->

    = 2,

   2sin(x)*cos(x) = 1  --->  sin(2x) = 1  --->  2x =   --->  x =   or  x = . 

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


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



2.  Having this, you have   =  = 1 + 1 = 2.

Solved.