If the angle `theta` be divided into two parts such that the tangent of one part is m times the tangent of the other, then prove that their difference `phi` is obtained fron the relation is `sin phi=abs(((m-1))/((m+1)))sin theta`

An angle theta is divided into two parts so that the ratio of the tangents of the parts is k, if the difference, sin phi = (k-1)/(k+1) sin theta

An angle theta is divided into two parts alpha " and " beta such that tan alpha : tan beta = x : y : " prove that ", sin (alpha - beta) =(x-y)/(x+y) sin theta.

If one root of the equation (x-1)(7-x)=m is three times the other, then m is equal to

A body of mass m is divided into two parts. The mass of one part is xm and that of the other part is (1-x) m. For a definite distance of separation between them, if the gravitational force of attraction has to be the maximum, the value of x should be

If sin theta sin phi - cos theta cos phi+1 =0 then the value of 1+ cot theta tan phi is-

For any two numbers theta and phi , we define theta R phi if and only if sec^(2) theta - tan ^(2) phi =1 the relation R is -

For any two real number theta and phi we define theta phi if and only if sec^2theta - tan^2theta=1 .the relation R is

If theta be the angle between two unit vectors vece_1 and vece_2 then prove that |vece_1 - vece_2| = 2 sin (theta/2)

If theta is the angle between the unit vectors veca and vecb , then prove that sin (theta/2)=1/2|veca-vecb|