`lim_(n->oo)(cosx+cos3x+cos5x+cos(2n-1)x)/n` where `x!=kpi, k in I`

lim_(x to 0) (cos5x-cos7x)/(cosx-cos5x)

Prove that cos x+cos3x+cos5x+cos(2n-1)x=(sin2nx)/(2)sin x

lim_(n rarr oo)([x]+[3x]+[5x]+[(2n-1)x])/(n^(2))

Q. int_0^pie^(cos^2x)( cos^3(2n+1) x dx, n in I

Q. int_0^pie^(cos^2x)( cos^3(2n+1) x dx, n in I

Let f(x)=lim_(m->oo){lim_(n->oo)cos^(2m)(n !pix)}, where x in Rdot Then the range of f(x)

Let f(x)=lim_(m->oo){lim_(n->oo)cos^(2m)(n !pix)}, where x in Rdot Then prove that f(x)={1, if x is rational and 0, if x is irrational

Let f(x)=lim_(m->oo){lim_(n->oo)cos^(2m)(n !pix)}, where x in Rdot Then prove that f(x)={1, if x is rational and 0, if x is irrational

If (x)=(cos x+i sin x)(cos3x+i sin3x)...(cos(2n-1)x+i sin(2n-1)x) then f(x) is

The value of lim_(nrarroo)(cos x cos .(x)/(2)cos.(x)/(4)..cos .(x)/(2^(n))) is equal to