Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is H
Step-by-step explanation:
From the question we are told that
The equation is [tex]\frac{\sqrt{1 - cos^2 (x)} }{sin(x)} + \frac{\sqrt{1 - sin^2 (x)} }{cos(x)}[/tex]
The domain for x is [tex]0 < x < \frac{\pi}{2}[/tex]
Gnerally the equation above is not continuous, when
[tex]sin (x) = 0[/tex]
=> [tex]x = 0[/tex]
And when [tex]cos(x) = 0[/tex]
=> [tex]x = \frac{\pi}{2}[/tex]
Generally from trigonometry identity
[tex]sin^2x + cos^2 x = 1[/tex]
So
[tex]sin^2 x = 1 - cos^2 (x)[/tex]
So
[tex]cos^2 x = 1 - sin^2 (x)[/tex]
=> [tex]\frac{\sqrt{sin^2 (x)} }{sin(x)} + \frac{\sqrt{ cos^2 (x )} }{cos(x)}[/tex]
=> [tex]1 + 1[/tex]
=> [tex]2[/tex]
