Question

Tan2x/1+tan2x+cot2x/1+cot2x=1

Answer 1

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$\frac{ {tan}^{2} x}{1 + {tan}^{2}x } + \frac{ {cot}^{2} x}{1 + {cot}^{2} x} \\ = \frac{ {tan}^{2} x}{ {sec}^{2}x } + \frac{ {cot}^{2}x }{ {csc}^{2}x } \\ = {tan}^{2}x {cos}^{2} x + {cot}^{2} x {sin}^{2}x \\ = \frac{ {sin}^{2}x }{ {cos}^{2}x } . {cos}^{2} x + \frac{ {cos}^{2}x }{ {sin}^{2}x} . {sin}^{2} x \\ = {sin}^{2} x + {cos}^{2} x \\ = 1$