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

JEE/Engineering Exams
Maths
Solution
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( 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 )
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