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In a ∆ABC, ANGLE C = 90°, then minimum value of tanA + tanB is - (1) 1 (2) 2 (3) 3 (4) 4

    In a ∆ABC, ANGLE C = 90°, then minimum value of tanA + tanB is -
(1)    1    (2)    2    (3)    3    (4)    4

Grade:12

1 Answers

Arjun Praveen
19 Points
8 years ago
(tanA + tanB)^2=tan^2(A) + tan^2(B) +2tanAtanB     (A + B=90)
But (tan90-A) = tanB = cotA      thus tanA*tanB=1 and tan^2(A)=cot^2(B)
therefore..
(tanA + tanB)^2=tan^2(A) + tan^2(B) +​ 2
                          =tan^2(A) + cot^2(A) + 2
 minimum value of a*tan^2(A)+b*tan^2(B) = 2*(root of a*b)
therefore minimum value of (tanA + tanB)^2= 2+2
  ….mum value of tanA + tanB=root of 4
                                                =2
 
 
 

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