Question

1/1+tan^2A + 1/1+cot^2A =1​

Answer 1

Hope it helps you plz mark as brilliant answer

Answer 2

$\displaystyle \sf{ \bold { To \: Prove \: - }} \\ \\ \sf{ \bold { \dfrac{ 1 }{ 1 + \tan^2A } + \dfrac{ 1 }{ 1 + \cot^2A } = 1 }} \\ \\ \sf{ \bold { \star Proof \: - }} \\ \\ \sf{ \bold { \dfrac{ 1 }{ 1 + \tan^2A } + \dfrac{ 1 }{ 1 + \cot^2A } = 1 }} \\ \\ \sf{ \bold { \implies { \dfrac{ 1 }{ 1 + \frac{ sin^2A}{cos^2A} } + \dfrac{1 }{ 1 + \frac{cos^2A}{sin^2A} } }}} \\ \\ \sf{ \bold { \implies { \dfrac{ cos^2 A }{ sin^2A + cos^2A } + \dfrac{ sin^2A }{ sin^2A + cos^2A } }}} \\ \\ \sf{ \bold { \therefore sin^2A + cos^2A = 1 }} \\ \\ \sf{ \implies {\bold { sin^2A + cos^2A }}} \\ \\ \sf{ \bold { \implies { \boxed { 1 } } }} \\ \\ \sf{ \bold { LHS = RHS }} \\ \\ \sf{ \bold { \hence Hence \: Proved \: ! }}$