1.

If A + B = 45°, show that (1 + tan A) (1 + tan B) = 2.

Answer»

A + B = 45° 

tan (A + B) = tan 45° = 1

(i.e) (tan A + tan B)/(1 - tan A tan B) = 1

tan A + tan B = 1 - tan A tan B ... (1) 

Now LHS = (1 + tan A) (1 + tan B) 

= tan A + tan B + tan A tan B + 1 

= (1 – tan A tan B) + (tan A tan B + 1) from (1) 

= 2 = RHS



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