[" b) Prove that for the catenary "],[qquad y=c cosh(x)/(c)]

The absolute minimum of y= c cosh (x/c) is

The length of normal at any point to the curve,y=c cosh((x)/(c)) is

The length of normal at any point to the curve, y=c cosh(x/c) is

Let P(x)=((x-a)(x-b))/((c-a)(c-b))c^(2)+((x-b)(x-c))/((a-b)(a-c))a^(2)+((x-c)(x-a))/((b-c)(b-a))b^(2) Prove that P(x) has the property that P(y)=y^(2) for all y in R .

Prove that cosh2x=2cosh^(2)x-1

Let P(x) equiv ((x-a)(x-b))/((c-a)(c-b)).c^2+((x-b)(x-c))/((a-b)(a-c)).a^2+((x-c)(x-a))/((b-c)(b-a)).b^2 Prove that P(x) has the properly that P(y) = y^2 for all y in R.

Prove that sinh(x-y) = sinh x cosh y - cosh x sinh y .

If in A B C , the distances of the vertices from the orthocentre are x, y, and z, then prove that a/x+b/y+c/z=(a b c)/(x y z)

If a,b, c and x, y, z are all positive and unequal, then prove that, (b+c)(c+a)(a+b)gt8abc .