SOLUTION: Does 1/sin^2x simplify to csc^2x? Thanks

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Question 974496: Does 1/sin^2x simplify to csc^2x? Thanks
Found 2 solutions by MathLover1, harpazo:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

yes, 1%2Fsin%5E2%28x+%29 simplify to csc%5E2%28x%29
recall reciprocal identities: sin%28x+%29=1%2Fcsc%28x%29 => csc%28x%29=1%2Fsin%28x+%29
so,square both sides of csc%28x%29=1%2Fsin%28x+%29 and you get
csc%5E2%28x%29=1%2Fsin%5E2%28x+%29

Answer by harpazo(655) About Me  (Show Source):
You can put this solution on YOUR website!
Does 1/sin^2x simplify to csc^2x?
Remember that sin^2x = 1/csc^2x.
Sine and cosecant as reciprocal identities.
Then the problem becomes 1 divided by 1/csc^2x, which is now a complex trigonometric fraction.
When we multiply the numerator and denominator by csc^2x, we end up with
simply csc^2x.
So, the answer to your question is yes.
1/sin^2x simplifies to csc^2x.