Question

If A+B= pie/4then prove that (1+TanA)(1+Tan B) = 2​

Answer 1

$\huge \sf \underline \red{Answer : }$

$\sf \underline \green{ \therefore \: (1 + tanA)(1 + tanB) = 2}$

$\huge \sf \underline \pink{Solution : }$

$\: \: \: \: \: \sf \underline{Given \:A+B = \dfrac{\pi}{4}}$

●$\sf \underline{Now \: take \: the \: tan \: on \: both \: sides \: we \: get}$

$\sf \implies{ \tan(A+B) = tan \dfrac{\pi}{4}}$

$\sf \implies{ tanA + \dfrac{tanB}{1 - tanA \: tanB = 1}}$

$\sf \implies{tanA + tanB = 1 - tanA \: tanB}$

$\sf \implies{tanA + tanB + tanA \: tanB = 1}$

●$\sf\underline{Now \: Add \: 1 \: both \: sides \: we \: get}$

$\sf \implies{1 + tanA \: + tanB + tanA \: tanB = 2}$

$\sf \implies{1(1 + tanA) + tanB(1 + tanA) = 2}$

$\sf \implies{(1 + tanA)(1 + tanB) = 2}$

$\sf \underline \red{ \therefore \: (1 + tanA)(1 + tanB) = 2}$

Answer 2

If A+B= pie/4then prove that (1+TanA)(1+Tan B) = 2

2