In an acute angled `triangle ABC`, the minimum value of `tanA tanB tan – InterviewSolution

InterviewSolution

1.	In an acute angled `triangle ABC`, the minimum value of `tanA tanB tanC` is
Answer» As, `tanAtanBtanC= tanA+ tanB + tanC`Since, `A.M ge G.M``(tanA+ tanB + tanC)/3 ge root(3)(tanAtanBtanC)``root(2/3)(tanA+ tanB + tanC) ge 3`So, `(tanA + tanB+ tanC) ge 3^(3/2)`Hence,` min(tanA + tanB+ tanC)= 3sqrt3`

Discussion

No Comment Found

Related InterviewSolutions

In an acute angled `triangle ABC`, the minimum value of `tanA tanB tanC` is
Consider the system of linear equations in `x , ya n dz :``""(sin3theta)x-y+z=0(cos2theta)x+4y+3z=0``3x+7y+7z=0`Which of the following can be the value of `theta`for which the system has a non-trivial solution`npi+(-1)^npi/6,AAn in Z``npi+(-1)^npi/3,AAn in Z``npi+(-1)^npi/9,AAn in Z`none of these
In `(0, 4pi)`, the number of solutions of `2sin^(2)theta=cos2theta` areA. `4`B. `2`C. `8`D. `6`
If `f(theta)=(1-sin2theta+cos2theta)/(2cos2theta)`, then value of `8f(11^0)*f(34^0)`is ____
If A = `4 sin theta + cos^(2) theta` , which of the following is not true ?(A) Maximum value of A is 5 .(B) Minimum value of A is `-4`(C) Maximum value of A occurs when `sin theta = 1//2`(D) Minimum value of A occurs when `sin theta = 1`.A. Maximum value of A is 5 .B. Minimum value of A is `-4`C. Maximum value of A occurs when `sin theta = 1//2`D. Minimum value of A occurs when `sin theta = 1`.
Show that the equation `sintheta=x+1/x`is not possible if `x`is real.
In `(0, 2pi)`, the number of solutions of `cos2theta=sintheta` areA. `1`B. `2`C. `3`D. `4`
Find the values of x for which `3costheta=x^2-8x+19` holds good.
Find the number of solution of `theta in [0,2pi]`satisfying the equation `((log)_(sqrt(3))tantheta(sqrt((log)_(tantheta)3+(log)_(sqrt(3))3sqrt(3))=-1`
If `sin alpha + sin beta = a and cos alpha + cos beta =b`, show that `sin(alpha+beta)=(2ab)/(alpha^2+beta^2)`