Question

( quad alpha+beta=frac{pi}{4} )
( Rightarrow tan (alpha+beta)=tan frac{pi}{4} )
( Rightarrow frac{tan alpha+tan beta}{1-tan alpha tan beta}=1 )
( Rightarrow tan alpha+tan beta=1-tan alpha tan beta )
( Rightarrow tan alpha+tan alpha tan beta+tan beta+1=1+1 )
( Rightarrow quad(1+tan alpha)(1+tan 3)=2 )

# (iii) If a + B prove that (1 + tan a) (1 + tan B) = 2.

Solution