can anybody please solve the foolowing problem?
(a2-4)1/2tanA+atanB+(a2+4)1/2tanC=6a
where a is a +ve prameter & A,B,C are arbtrary angles
find the max & min value of the expression tan2A+tan2B+tan2C
what is the role of tan here? You can as well call tanA, tanB, tanC as some x,y,z.. it doesnt affect the condition or the result..
Let us consider the equation as ax + by + gz = d where d > 2 and x,y,z ε R
This is the equation of a plane at a distance d from the origin.We are required to find the maximum and minimum values of x2 + y2 + z2 Let x2 + y2 + z2 = s2
This is obviously the equation of a sphere with centre (0,0,0) and radius ‘s ’, which in our case, is variable.
Thus, the problem is condensed to finding the minimum and maximum distances of a point on the plane from the origin. Thus we get,minimum value of s = d = 6a è min(s2) = 36a2 and
maximum value of S = infinity => max(s2)= infinity