Q64 of 76 Page 52

Fill in the blanks

In a triangle ABC with ∠C = 90° the equation whose roots are tan A and tan B is ________.


[Hint: A + B = 90°⇒ tan A tan B = 1 and tan A + tan B ]

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)


Now,







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



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