If for all real values of ua n dv ,2f(u)...

If for all real values of `ua n dv ,2f(u)cosv=(u+v)+f(u-v),` prove that for all real values of `x ,` `f(x)+f(-x)=2acosxdot` `f(pi-x)+f(-x)=0` `f(pi-x)+f(x)=2bsinxdot` Deduce that `f(x)=acosx+bsinx ,w h e r ea ,b` are arbitrary constants.

Similar Questions

Explore conceptually related problems

H(x) increase as f(x) decreases for all real values of x if

Let f be a real-valued function such that f(x)+2f((2002)/x)=3xdot Then find f(x)dot

If a function f satisfies f (f(x))=x+1 for all real values of x and if f(0) = 1/2 then f(1) is equal to

If f is a real valued function such that f(x+y) = f(x) + f(y) and f(1)=5, then the value of f(100) is

Consider the real function f(x ) = ( x+2)/( x-2) prove that f(x) f(-x) +f(0) =0

f is a real valued function from R to R such that f(x)+f(-x)=2 , then int_(1-x)^(1+X)f^(-1)(t)dt=

If f (x) satisfies the relation 2 f(x ) + f(1-x) =x^2 for all real x, then f (x) is

Let f (x) be a quadratic expressinon which is positive for all real values of x, If g(x)=f(x)+f'(x)+f''(x), then for any real x

If f(x+y)=f(x)dotf(y) for all real x , ya n df(0)!=0, then prove that the function g(x)=(f(x))/(1+{f(x)}^2) is an even function.

If u=f(x^3),v=g(x^2),f^(prime)(x)=cosx ,a n dg^(prime)(x)=sinx ,t h e n(d u)/(d v) is