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

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) (Show Source): You can put this solution on YOUR website!
...........since , we have

Answer by DrBeeee(684) (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
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