Let $f(x)=\sin x$ and $g(x)=\cos x, x \in \mathbb{R}$. Define $h(x)=\frac{f(g(x))}{g(f(x))}$. Then

• A

  $h(x) \gt 0$ wherever $h(x)$ is well-defined
• Correct answer
  B

  domain of $\frac{1}{h(x)}$ is $\left\{x \in \mathbb{R}: x \neq(2 n+1) \frac{\pi}{2}, n \in \mathbb{Z}\right\}$
• Correct answer
  C

  domain of $h(x)$ is $\mathbb{R}$
• Correct answer
  D

  $h(x) \lt 1$ wherever $h(x)$ is well-defined

Hence, the correct answer is options: 'B', 'C', 'D'.