NeroKid said:you can use the langrange function to do it, it is quite easy if u use it
Michael_Light said:1. Given a,b,c are acute angles and a + b + c =180. find the minimum of tan(a).tan(b).tan(c)
ehild said:Following rock.freak's suggestion, I would write the tangent of the third angle in terms of the tangents of the other two angles, and would use the relation between geometric and arithmetic means.
ehild
NeroKid said:tan(a)*tan(b)*tan(c) = -tan(b+c) *tan(b)*tan(c) = (tanb+tanc)/(1-tanb*tanc) *tanb*tanc
call S = tanb + tanc and P = tanb * tanc S^2>= 4P this should be easy from here on
Michael_Light said:Still cannot do...
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.
The minimum value of tan(a).tan(b).tan(c) is 0. This occurs when one of the angles (a, b, or c) is equal to 0 degrees.
To find the minimum value of tan(a).tan(b).tan(c), you can use the trigonometric identities and properties such as the fact that tan(0) = 0 and the product-to-sum identity for tangent.
Finding the minimum value of tan(a).tan(b).tan(c) can be useful in solving optimization problems, where the goal is to minimize a certain quantity. It can also be used in trigonometric equations and applications involving triangles.
No, the minimum value of tan(a).tan(b).tan(c) cannot be negative. This is because the tangent function is always positive in the first and third quadrants, and when one of the angles is equal to 0 degrees, the product of the tangents will be 0.