If `A >0,B >0a n dA+B=pi/3,` the maximum value of `tanAtanB` is______

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

If y = tan^(-1).(1)/(2) + tan^(-1) b, (0 b lt 1) and 0 lt y le (pi)/(4) , then the maximum value of b is

If an a triangle A B C , b=3ca n d C-B=90^0, then find the value of tanB

If ab=2a+3b, agt0, b gt0 , then the minimum value of ab is

In a triangle A B CifB C=1a n dA C=2, then what is the maximum possible value of angle A ?

If cot^(-1)n/pi>pi/6,n in N , then the maximum value of n is 6 (b) 7 (c) 5 (d) none of these

Vertices of a variable acute angled triangle A B C lies on a fixed circle. Also, a ,b ,ca n dA ,B ,C are lengths of sides and angles of triangle A B C , respectively. If x_1, x_2a n dx_3 are distances of orthocenter from A ,Ba n dC , respectively, then the maximum value of ((dx_1)/(d a)+(dx_2)/(d b)+(dx_3)/(d c)) is -sqrt(3) b. -3sqrt(3) c. sqrt(3) d. 3sqrt(3)

If aa n db are positive numbers and eah of the equations x^2+a x+2b=0a n dx^2+2b x+a=0 has real roots, then the smallest possible value of (a+b) is_________.

If y=f(x) is a monotonic function in (a,b), then the area bounded by the ordinates at x=a, x=b, y=f(x) and y=f(c)("where "c in (a,b))" is minimum when "c=(a+b)/(2) . "Proof : " A=int_(a)^(c)(f(c)-f(x))dx+int_(c)^(b)(f(c))dx =f(c)(c-a)-int_(a)^(c)(f(x))dx+int_(a)^(b)(f(x))dx-f(c)(b-c) rArr" "A=[2c-(a+b)]f(c)+int_(c)^(b)(f(x))dx-int_(a)^(c)(f(x))dx Differentiating w.r.t. c, we get (dA)/(dc)=[2c-(a+b)]f'(c)+2f(c)+0-f(c)-(f(c)-0) For maxima and minima , (dA)/(dc)=0 rArr" "f'(c)[2c-(a+b)]=0(as f'(c)ne 0) Hence, c=(a+b)/(2) "Also for "clt(a+b)/(2),(dA)/(dc)lt0" and for "cgt(a+b)/(2),(dA)/(dc)gt0 Hence, A is minimum when c=(a+b)/(2) . If the area bounded by f(x)=(x^(3))/(3)-x^(2)+a and the straight lines x=0, x=2, and the x-axis is minimum, then the value of a is

If y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5, then the value of (a^2)/(b^2) is_______