If an angle `alpha` be divided into two parts such that the ratio of tangents of the parts is K. If x be the difference between the two parts , then prove that `sinx = (K-1)/(K+1) sin alpha`.

Divide 29 into two parts so that the sum of the squares of the parts is 425.

Divide 64 into two parts such that the sum of the cubes of two parts is minimum.

Divide 108 in two parts in the ratio 4: 5.

Divide 16 into two parts such that the sum of their cubes is minimum.

If angle theta is divided into two parts such that the tangents of one part is lambda times the tangent of other, and phi is their difference, then show that sintheta=(lambda+1)/(lambda-1)sinphi .

Charge Q is divided into two parts which are then kept some distance apart . The force between them will be maximum if the two parts are

Divide 20 into two parts such that the product of one part and the cube of the other is maximum. The two parts are

If an angle theta is divided into two parts A and B such that A-B=x and tanA :tanB=k :1 , then the value of sinx is

A+ B = C and tan A = k tan B , then prove that sin (A-B) = (k-1)/(k+1) sin C

Divide 16 into two parts such that twice the square of the larger part exceeds the square of the smaller part by 164.