If in a `DeltaABC`, the side c and the angle C remain constant, while the remaining elements are changed slightly. Using differential, show that `(da)/(cosA)+(db)/(cosB)=0`.

If in a triangle A B C , the side c and the angle C remain constant, while the remaining elements are changed slightly, using differentials show that (d a)/(c sA)+(d b)/(cosB)=0

If the sides and angles of a plane triangle vary in such a way that its circumradius remains constant then that (da)/cosA+(db)/cosB+(dc)/cosC=

If a triangle ABC, inscribed in a fixed circle, be slightly varied in such away as to have its vertices always on the circle, then show that (d a)/(c a sA)+(d b)/(cosB)+(d c)/(cosC)=0.

In an acute triangle A B C if sides a , b are constants and the base angles Aa n dB vary, then show that (d A)/(sqrt(a^2-b^2sin^2A))=(d B)/(sqrt(b^2-a^2sin^2B))

For hyperbola x^2sec^2alpha-ycos e c^2alpha=1, which of the following remains constant with change in 'alpha'

The internal bisectors of the angles of a DeltaABC meet the sides BC, CA, AB in D,E and F, respectively. Show that the area of the DeltaDEF is equal to, (2Deltaabc)/((b+c)(c+a)(a+b))

If two adjacent sides of a cyclic quadrilateral aré 2 and 5 and the angle between them is 60°. If the third side is 3, then the remaining fourth side is (a) 2 (b) 3 (c) 4 (d) 5

Hydrolysis of methyl acetate in aqueous solution has been studied by titrating the liberated acetic acid against sodium hydroxide. The concentration of the ester at different times is given below. Show that it follows a pseudo first order reaction, as the concentration of water remains nearly constant (55 mol L^(-1)), during the course of the reaction. What is the value of k in this equation? Rate = k [CH_3C00CH_3][H_20]

Select the correct statement(s): a) Mass number remains constant when positron emission takes place b) One neutron converts into proton in beta(._(-1)^(0)e) emission process c) Activity of a radioactive substance double when temp. increases from 300 K to 310 K d) Isodiaphers formed when one alpha particle emitted and isotopes formed when 2 beta particles emitted

If the sine of the angles of DeltaABC satisfy the equation c^(3)x^(3)-c^(2) (a+b+c)x^(2)+lx +m=0 (where a,b,c are the sides of DeltaABC), then DeltaABC is