Answer :

Given that, a ΔABC with C = 90° and an equation whose roots are tan A and tan B

x2 – (tan A + tan B)x + tan A. tan B = 0 (i)

Now, A+B = 90° [ C = 90°]

tan(A+B) = tan90°

1-tan A tan B = 0

tan A tan B = 1 (ii)


Substituting the values from (ii) and (iii) in equation (i), we get

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