The complete set of values of $\text{'}a\text{'}$ for which the function $f\left(x\right)=\left(a+2\right)x^3-3a{x}^2+9ax-1$ decreases for all real values of $x$ is

Which of the following statement is/are true ?

(1) $f\left(x\right)=\sin x$ is increasing in interval $\left[\frac{-\pi }{2},\frac{\pi }{2}\right.⌋$
(2)$f\left(x\right)=\sin x$ is increasing at all point of the interval $\left[\frac{-\pi }{2},\frac{\pi }{2}\right]$
(3) $f\left(x\right)=\sin x$ is increasing in interval $\left(\frac{-\pi }{2},\frac{\pi }{2}\right)\cup \left(\frac{3\pi }{2},\frac{5\pi }{2}\right)$
(4) $f\left(x\right)=\sin x$ is increasing at all point of the interval $\left(\frac{-\pi }{2},\frac{\pi }{2}\right)\cup \left(\frac{3\pi }{2},\frac{5\pi }{2}\right)$
(5) $f\left(x\right)=\sin x$ is increasing in intervals $\left[\frac{-\pi }{2},\frac{\pi }{2}\right]\cup \left[\frac{3\pi }{2},\frac{5\pi }{2}\right]$

STATEMENT-$1$: $e^{\pi }$ is bigger than ${\pi }^e$.

STATEMENT-$2$: $f\left(x\right)=x^{\frac{1}{x}}$ is a increasing function when $x\in [e,\infty )$.