CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

If A>0,B>0 and A+B=π3, then the maximum value of 3tanAtanB is


Solution

Let y=tanAtanB,
So A,B>0 and A+B=π3A,B<π3
tanAtanB<3y(0,3)(i)
Now
A+B=π3tan(A+B)=3
tanA+tanB1tanAtanB=3
tanA+ytanA1y=3
tan2A+3(y1)tanA+y=0
For real +ive value of tanA,
3(y1)24y0
3y210y+30
(y3)(y13)0
y(,13][3,)(ii)
from (i) and (ii) y(0,13]
So,  maximum value of 3y is 1.
 

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More


People also searched for
View More



footer-image