Question

If A > 0, B > 0 and A + B = pi/3, then the maximum value of tan A tan B is .....

Answer 1

Answer:

Step-by-step explanation:

B = pi/3 - A  

so that tan(B) = tan(pi/3 - A)  

= (tan(pi/3) - tan(A))/(1 + tan(pi/3)tan(A))  

=(sqrt(3) - tan(A))/(1 + sqrt(3)tan(A))  

y = (sqrt(3)tan(A) - tan^2(A))/(1 + sqrt(3)tan(A))  

max y when dy/dA = 0  

dy/dA = [(sqrt(3)sec^2(A) - 2tan(A)sec^2(A))(1 + sqrt(3)tan(A)) - sqrt(3)sec^2(A)(sqrt(3)tan(A) - tan^2(A))]/(1 + sqrt(3)tan(A))^2  

etc etc