Question 1057489
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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 &nbsp;&nbsp;tan(A) + cot(A) = 1 &nbsp;&nbsp;<U>THEN</U>&nbsp;&nbsp; tan(A) = 1  &nbsp;&nbsp;and &nbsp;&nbsp;cot(A) = 1 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(see the theorem below)


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


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<H3>Theorem</H3>If &nbsp;{{{x + 1/x}}} = 2 &nbsp;&nbsp;and &nbsp;x&nbsp; is a real number &nbsp;<U>THEN</U>&nbsp; x = 1.


<U>Proof</U>

If &nbsp;{{{x + 1/x}}} = 2 &nbsp; then it is clear that x is positive and you can take {{{sqrt(x)}}}.


Then you can rewrite the equality &nbsp;{{{x + 1/x}}} = 2 &nbsp; in an equivalent form

{{{(sqrt(x))^2 - 2}}} + {{{(1/sqrt(x))^2}}} = 0,   or, equivalently,

{{{(sqrt(x) - 1/sqrt(x))^2}}} = 0.


It implies {{{sqrt(x)}}} = {{{1/sqrt(x)}}},  or  {{{(sqrt(x))^2}}} = 1.

Hence, {{{sqrt(x)}}} = 1 and, therefore, x = 1.


QED.
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