## anonymous one year ago How can I show that the function y=(cos^-1)x satisfies the equation [(d^2y)/(dx^2)]=-cot y cosec^2 y?

1. anonymous

|dw:1443184414753:dw| I tried subbing y into the equation, is that what I'm meant to do?

2. IrishBoy123

yes you did $$\cos y = x$$ implicitly?

3. anonymous

@IrishBoy123 You mean like this: |dw:1443185241885:dw|

4. IrishBoy123

well, no, i was thinking doing it this way: $$\cos y = x$$ $$-sin y \, y' = 1$$ $$- \cos y \, (y')^2 - \sin y \, y' \, y '' = 0$$ then rearranging all of that.

5. anonymous

Oh that makes sense, thank you so much! :)

6. IrishBoy123

typo in last line $$- \cos y \, (y')^2 - \sin y \, y '' = 0$$