Answer:
Option 1 is correct.
Step-by-step explanation:
Given two functions f(x)=sec x and g(x)=arcsin x
we have to find f(g(x)).
f(g(x))=sec(arcsinx)=sec A where A=arc(sinx)
As, A=arc(sinx)
⇒ [tex]x=sin A=\frac{P}{H}[/tex]
⇒ P=x and H=1 gives [tex]B=\sqrt{1-x^2}[/tex]
hence, [tex]sec A=\frac{H}{B}=\frac{1}{\sqrt{1-x^2}}[/tex]
hence, [tex]f(g(x))=\frac{1}{\sqrt{1-x^2}}[/tex]
Rationalizing, we get
[tex]f(g(x))=\frac{\sqrt{1-x^2}}{1-x^2}[/tex]
Option 1 is correct.
