If x and y are acute angles and `cosx=(13)/(14)andcosy=(1)/(7)` then prove that `x-y=-(pi)/(3)`.

If a, b, x, y are positive natural numbers such that (1)/(x) + (1)/(y) = 1 then prove that (a^(x))/(x) + (b^(y))/(y) ge ab .

If x and y are positive acute angles such that (x+y) and (x-y) satisfy the equation tan^(2) theta - 4 tan theta +1=0 , then

y= sqrt((1- sin 2x)/(1+ sin 2x)) then prove that (dy)/(dx) + sec^(2) ((pi)/(4)-x)= 0

The measure of the angle between the curves y=2 sin^(2)x and y = cos 2 x at x=(pi)/(6) is ……….

If x,y, z are three consecutive terms of a G.P. then prove that (1)/(x+y) + (1)/(y+ z)= (1)/(y) .

y=[log(x+sqrt(x^2+1))]^2 then prove that (x^2+1)y_2+x y_1=2

If y= (x + sqrt(x^(2) + 1))^(m) then prove that, (x^(2)+1) y_(2) + xy_(1)= m^(2)y

If A(x_(1), y_(1)), B(x_(2), y_(2)) and C (x_(3), y_(3)) are the vertices of a Delta ABC and (x, y) be a point on the internal bisector of angle A, then prove that b|(x,y,1),(x_(1),y_(1),1),(x_(2),y_(2),1)|+c|(x,y,1),(x_(1),y_(1),1),(x_(3),y_(3),1)|=0 where, AC = b and AB = c.

Prove that (sinx-siny)/(cosx+cosy)=tan((x-y)/(2))

Find the angle between the lines (x+1)/(2)=(y)/(3)=(z-3)/(6) and the planes 3x+y+z=7 .