SOLUTION: For the expression below, write an equivalent expression that involves x only. Assume x is positive. csc(sin^-1(1/x))

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Question 769293: For the expression below, write an equivalent expression that involves x only. Assume x is positive.
csc(sin^-1(1/x))
Found 2 solutions by MathLover1, DrBeeee:
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
csc%28sin%5E-1%281%2Fx%29%29...........since +%28sin%5E-1%281%2Fx%29%29=csc%5E%28-1%29%28x%29, we have

csc%28csc%5E%28-1%29%28x%29%29=x

Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
(1) csc(y) = csc(arcsin(1/x)), where I use the equivalent notation arcsin(z) = sin^(-1)z. Comparing the left side to the right side we see that
(2) y = arcsin(1/x) or
(3) sin(y) = 1/x
Now use the identity
(4) csc(y) = 1/sin(y) and (3) we get
(5) csc(y) = 1/(1/x) or
(6) csc(y) = x
Answer: csc(arcsin(1/x) = x