If `f(x)=cos(logx)`, then prove that
`f((1)/(x)).f((1)/(y))-(1)/(2)[f((x)/(y))+f(xy)]=0`

If f(x)=cos(logx) , then f(x^(2))f(y^(2))-(1)/(2)[f(x^(2)y^(2))+f((x^(2))/(y^(2)))]=

If f(x)=cos((log)_e x),\ t h e n\ f(1/x)f(1/y)-1/2{f(x y)+f(x/y)} is equal to a. "cos"(x-y) b. log(cos(x-y)) c. 0 d. "cos"(x+y)

If f(x)=cos(logx), then value of f(x) f(4)-1/2{f(x/4)+f(4x)} is (a) 1 (b) -1 (c) 0 (d) +- 1

If f(x) = (1 + x)/(1 - x) Prove that ((f(x) f(x^(2)))/(1 + [f(x)]^(2))) = (1)/(2)

If f(x) = cos(log x) then f(x)f(y)-1/2[f(x/y)+f(xy)] has the value

If f(x) = x/(x-1)=1/y then the value of f(y) is

If f(x)=sin(logx) then f(xy)+f(x/y)-2f(x)cos(logy)= (A) cos(logx) (B) sin(logy) (C) cos(log(xy)) (D) 0

let f(x)=sqrt(1+x^2) then (i) f(xy)=f(x)*f(y) (ii) f(xy)gef(x)*f(y) (iii) f(xy)lef(x)*f(y) (iv) None of these

If any differentisl equation in the form f(f_(1)(x,y)d(f_(1)(x,y)+phi(f_(2)(x,y)d(f_(2)(x,y))+....=0 then each term can be intergrated separately. For example, intsinxyd(xy)+int((x)/(y))d((x)/(y))=-cos xy+(1)/(2)((x)/(y))^(2)+C The solution of the differential equation (xy^(4)+y)dx-xdy=0 is

If any differential equation in the form f(f_(1)(x,y)d(f_(1)(x,y)+phi(f_(2)(x,y)d(f_(2)(x,y))+....=0 then each term can be intergrated separately. For example, intsinxyd(xy)+int((x)/(y))d((x)/(y))=-cos xy+(1)/(2)((x)/(y))^(2)+C Solution of differential equation (2xcosy+y^(2)cosx)dx+(2ysinx-x^(2)siny)dy=0 is