" 7.If "x=(3)/(7)" and "y=-(1)/(2)," then prove that ":|x+y|<|x|+|y|

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

If x and y are acute angles such that cos x=(13)/(14) and cosy =(1)/(7), prove that (x-y)=(pi)/(3)

"If "y=x+x^(2)+x^(3)+...oo and |x|lt1, "then prove that "x=(y)/(1+y).

"If "y=x+x^(2)+x^(3)+...oo and |x|lt1, "then prove that "x=(y)/(1+y).

If (3.7)^x=(.37)^y=1000 ,then prove that 1/x-1/y=1/3

If log((x+y)/3)=1/2(logx+logy) ,then prove that x/y+y/x=7

y=(x)/(1+(x)/(2+(x)/(1+(x)/(2)+...))) then prove that y'=(1)/(1+y)

If the tangent at (x_(1),y_(1)) to the curve x^(3)+y^(3)=a^(3) meets the curve again in (x_(2),y_(2)), then prove that (x_(2))/(x_(1))+(y2)/(y_(1))=-1

If x prop y and y prop z , then prove that (x^7+y^7 +z^7) prop (x^5y^2 +x^3z^4 +y^5z^2)

If x!=y!=z and |x x^2 1+x^3 y y^2 1+y^3 z z^2 1+z^3|=0 , then prove that x y z=-1 .