SOLUTION: tanA+cotA=2 but how to find the value of A nd in your answee tan^2+1-2tanA=0 nd next step is tanA = 1 how u can do the step can u explain plzz

Question 1057489: tanA+cotA=2 but how to find the value of A nd in your answee tan^2+1-2tanA=0 nd next step is tanA = 1 how u can do the step can u explain plzz

Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
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tanA+cotA=2 but how to find the value of A nd in your answee tan^2+1-2tanA=0 nd next step is tanA = 1 how u can do the step can u explain plzz
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If   tan(A) + cot(A) = 1   THEN   tan(A) = 1   and   cot(A) = 1       (see the theorem below)

        and, as a consequence, A = 45 degs   OR   A = 225 degs.

Theorem
If   = 2   and  x  is a real number  THEN  x = 1.


Proof

If   = 2   then it is clear that x is positive and you can take .


Then you can rewrite the equality   = 2   in an equivalent form

 +  = 0,   or, equivalently,

 = 0.


It implies  = ,  or   = 1.

Hence,  = 1 and, therefore, x = 1.


QED.

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