How do you prove that ${tan}^{2} A + {cot}^{2} A = 1$ $tan^2A+cot^2A=1$ is not an identity by showing a counterexample?

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Answer 1 · 2016-12-23T08:35:39

It makes A unreal.

This is another form of ${sin}^{2} (2 A) = \frac{4}{3}$ $sin^2(2A)= 4/3$ that implies

$| sin (2 A) | = \frac{2}{\sqrt{3}} > 1 .$ $|sin (2A)|=2/sqrt3 >1.$

So, A is unreal.

How do you prove that tan2A+cot2A=1tan^2A+cot^2A=1 is not an identity by showing a counterexample?