Question

tan 2 A / 1 + tan 2 + cot 2 A / 1 + cot 2 A = 1​

Answer 1

Step-by-step explanation:

$lhs = \frac{ { \tan }^{2}A }{1 +{ \tan }^{2}A } + \frac{ { \cot }^{2}A }{1 +{ \cot }^{2}A} \\ \\ = \frac{ { \tan }^{2}A }{1 +{ \tan }^{2}A } + \frac{ \frac{1}{{ \tan }^{2}A} }{1 +\frac{1}{{ \tan }^{2}A}} \\ \\ = \frac{ { \tan }^{2}A }{1 +{ \tan }^{2}A } + \frac{ \frac{1}{{ \tan }^{2}A} }{\frac{{ \tan }^{2}A \: + 1 }{{ \tan }^{2}A}} \\ \\ = \frac{ { \tan }^{2}A }{1 +{ \tan }^{2}A } + \frac{ 1 }{1 +{ \tan }^{2}A } \\ \\ = \frac{ { \tan }^{2}A + 1}{1 +{ \tan }^{2}A } \\ \\ = 1 \\ = rhs$