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` .

Divide 184 into two parts such that one-third of one part may exceed one-seventh of the other part by 8.

Divide 184 into two parts such that one-third of one part may exceed one-seventh of the other part by 8.

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

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 .

A positive acute angle is divided into two parts whose tangents are 1/2 and 1/3. Show that the angle is (pi)/(4).

If the tangents from the point (lambda, 3) to the ellipse x^2/9+y^2/4=1 are at right angles then lambda is

If the direction ratios of a line are 1+lambda, 2-lambda, 4 and if it makes an angle of 60^(@) with the y- axis, then the sum of the values of lambda is

Circles with radii 3, 4 and 5 touch each other externally. If P is the point of intersection of tangents to these circles at their points of contact, then if the distance of P from the points of contact is lambda then lambda_2 is _____

Out of the two roots of x^(2)-2 lambda x + lambda^(2)-1= 0 , one is greater than 4 and the other root is less than 4, then the limits of lambda are