Question

9. If A + B = 45°, then (1 + tan A)(1 + tan B) =​

Answer 1

hope it will help you :-)

Answer 2

AnswEr:

$\bold{\underline{\sf{\red{Given}}}}$

$:\implies\sf\; A + B = 45$

$\bold{\underline{\sf{Taking\; tan\; on\; Both\; Sides}}}$

$:\implies\sf\; tan(A + B) = 45 = tan = 45$

$:\implies\sf\; \dfrac{ tan A + tan B}{1 - tan A tan B}= 1$

$:\implies\sf\; tan A + tan B = 1 - tan A tan B$

$\bold{\underline{\sf{Adding\; 1 \; Both\; Sides}}}$

$:\implies\sf\; tan A + tanA + tan B + tan B + 1 = 1 + 1$

$:\implies\sf\; tan ( 1 + tan B) + 1 (tan B + 1) = 2$

$:\implies\large{\underline{\boxed{\sf{\blue{ (1 + tan A) (1 + tan B) = 2}}}}}$

$\rule{150}3$