Two tiny spheres each having mass mkg and charge q coulomb are suspended from a point by insulating threads each l metre long but negligible `theta` with the vertical.
Prove that, `q^(2)=(4mgl^(2)sin^(2)theta tan theta)4pi epsilon_(0)`

Prove that: (cos2theta)/(1+sin2theta)=tan(pi/4-theta)

Prove that (cos2theta)/(1+sin2theta)=tan(pi/4-theta) .

Two particles, each of mass m and carrying a charge q, are suspended from a point by insulated strings each of length 1 cm. In equilibrium each string makes an angle of 45^(@) with the horizontal direction. Prove that, q=sqrt(2mg) , g = acceleration due to gravity.

Two identical spheres, each of mass m, are suspended from a point by threads. Each sphere carries a charge q. If the angle between the threads is very small, prove that in equilibrium, the distance between the centres of the two spheres is, x=((q^(2)l)/(2pi epsilon_(0)mg))^((1)/(3))

Two spheres, each having mass m are suspended from a common point by two insulating strings of length l. The spheres are identically charged and the separation between the spheres is 'd' . Find the charge on each sphere.

Prove that: (costheta)/(1+sintheta)=tan(pi/4-theta/2)

Prove that tan(pi//4+theta)-tan(pi//4-theta)=2tan2theta

Show that int_0^(pi/2)sqrt((sin2theta))sintheta d theta=pi/4

The value of int_(0)^((pi)/(4))tan^(2)thetad theta is-

If tan theta+sin theta=m and tan theta-sin theta=n , prove that, mn=tan^2sin^2theta and m^2-n^2=4sqrt(mn)(mgtn) .