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

Algebra ->  Trigonometry-basics -> 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       Log On


   

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(52781) About Me  (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  x+%2B+1%2Fx = 2   and  x  is a real number  THEN  x = 1.


Proof

If  x+%2B+1%2Fx = 2   then it is clear that x is positive and you can take sqrt%28x%29.


Then you can rewrite the equality  x+%2B+1%2Fx = 2   in an equivalent form

%28sqrt%28x%29%29%5E2+-+2 + %281%2Fsqrt%28x%29%29%5E2 = 0,   or, equivalently,

%28sqrt%28x%29+-+1%2Fsqrt%28x%29%29%5E2 = 0.


It implies sqrt%28x%29 = 1%2Fsqrt%28x%29,  or  %28sqrt%28x%29%29%5E2 = 1.

Hence, sqrt%28x%29 = 1 and, therefore, x = 1.


QED.