Let $$f(x)=2+\cos x$$ for all real $$x$$.

STATEMENT - 1 : For each real $$t$$, there exists a point $$c$$ in $$[t, t+\pi]$$ such that $$f^{\prime}(C)=0$$.

STATEMENT - 2 : $$f(t)=f(t+2 \pi)$$ for each real $$t$$.

Lines $$\mathrm{L}_{1}: y-x=0$$ and $$\mathrm{L}_{2}: 2 x+y=0$$ intersect the line $$\mathrm{L}_{3}: y+2=0$$ at $$\mathrm{P}$$ and $$\mathrm{Q}$$, respectively. The bisector of the acute angle between $$L_{1}$$ and $$L_{2}$$ intersects $$L_{3}$$ at $$R$$.

STATEMENT - 1 : The ratio PR : RQ equals $$2 \sqrt{2}: \sqrt{5}$$.

STATEMENT - 2 : In any triangle, bisector of an angle divides the triangle into two similar triangles.

Let $$\mathrm{A_{1}, G_{1}}, \mathrm{H}_{1}$$ denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For $$n \geq 2$$, let $$\mathrm{A}_{n-1}$$ and $$\mathrm{H}_{n-1}$$ have arithmetic, geometric and harmonic means as $$\mathrm{A_{n}}$$, $$\mathrm{G}_{\mathrm{n}}, \mathrm{H}_{\mathrm{n}}$$ respectively.

Which one of the following statements is correct?

Let $$\mathrm{A_{1}, G_{1}}, \mathrm{H}_{1}$$ denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For $$n \geq 2$$, let $$\mathrm{A}_{n-1}$$ and $$\mathrm{H}_{n-1}$$ have arithmetic, geometric and harmonic means as $$\mathrm{A_{n}}$$, $$\mathrm{G}_{\mathrm{n}}, \mathrm{H}_{\mathrm{n}}$$ respectively.

Which one of the following statements is correct?