IF the tangents of the angles of a triangle are in A.P, prove that the squares of the sides are in the proportion `x^2(x^2+9):(3+x^2)^2:9(1+x^2)` where x is the least or the greates tangent.

The sides of a triangle are x^2+x+1, 2x+1 and x^2-1. Prove that the greatest angle is 120^0

The sides of a triangle are x^2+x+1,2x+1,a n dx^2-1 . Prove that the greatest angle is 120^0dot

If the sides of a triangle are in A.P., and its greatest angle exceeds the least angle by alpha , show that the sides are in the ratio 1+x :1:1-x , , where x = sqrt((1- cos alpha)/(7 - cos alpha))

Prove that the tangents to the curve y=x^2-5x+6 at the points (2, 0) and (3, 0) are at right angles.

The product of the sines of the angles of a triangle is p and the product of their cosines is qdot Show that the tangents of the angles are the roots of the equation q x^3-p x^2+(1+q)x-p=0.

Prove that the coefficient of x^3 in the expansion of (1+x+2x^2) (2x^2 - 1/(3x))^9 is -224/27.

The sides of a triangle ABC are (x^(2) + x +1),(2x+1) and (x^(2)-1) . Find the greatest angle of the triangle.

The lengths of the sides of an isosceles triangle are 9+x^2,9+x^2 and 18-2x^2 units. Calculate the area of the triangle in terms of x and find the value of x which makes the area maximum.

The area of the triangle formed with coordinate axes and the tangent at (x_(1),y_(1)) on the circle x^(2)+y^(2)=a^(2) is

Find the equations of the tangent and the normal to 16 x^2+9y^2=144 at (x_1,\ y_1) where x_1=2 and y_1>0 .