A %2B B = 45 ^ \circ , \text Show that ( 1 %2B \operatorname

1.	A %2B B = 45 ^ \circ , \text Show that ( 1 %2B \operatorname tan A ) ( 1 %2B \operatorname tan B ) = 2
Answer» Given A+B=45 {Take tan on both the sides } tan(A+B) = tan45 tanA+tanB/1- tanA tanB = 1 tanA+tanB=1-tanA.tanB tanA+tanB+tanA.tanB=1 adding "1" on both sides 1+ tanA+tanB+tanA.tanB=1+1 (1 + tanA)+tanB(1+tanA).=2 (1+tanA)(1+tanB)=2 Hence proved .

A %2B B = 45 ^ \circ , \text Show that ( 1 %2B \operatorname tan A ) ( 1 %2B \operatorname tan B ) = 2

Answer»

Given A+B=45 {Take tan on both the sides }

tan(A+B) = tan45

tanA+tanB/1- tanA tanB = 1

tanA+tanB=1-tanA.tanB

tanA+tanB+tanA.tanB=1

adding "1" on both sides

1+ tanA+tanB+tanA.tanB=1+1

(1 + tanA)+tanB(1+tanA).=2

(1+tanA)(1+tanB)=2 Hence proved .