Question

Which equation is correct?

Answer 1

Answer:

D) arccsc (x) = arcsin (1/x)

Step-by-step explanation:

Here's how you can prove it: Consider a right triangle with hypotenuse 1 and a side length 1/x.  If θ is the angle opposite of 1/x, then:

sin θ = 1/x

and

csc θ = x

Solving for θ:

θ = arcsin (1/x)

θ = arccsc (x)

Therefore:

arccsc (x) = arcsin (1/x)