## En one year ago prove the formula: arccos x=1/2pi- arcsin x please i still dont get it

1. EmmaTassone

do you know a bit of calculus?

2. En

yep :) i'm solving bunch of problems .. i just dont get this one.. :/

3. En

sorry for the trouble :)

4. EmmaTassone

$-\frac{ 1 }{ \sqrt{1-x²} }+\frac{ 1 }{ \sqrt {1-x²} }=0$ $\int\limits_{}^{}-\frac{ 1 }{ \sqrt{1-x²} } dx+\int\limits_{}^{}\frac{ 1 }{ \sqrt {1-x²} }dx=0$ $\arccos(x)+\arcsin(x)+\delta =0$ Where delta is a constant, evaluating in zero: $\arccos(0)+\arcsin(0)+\delta=0$ $\frac{ \pi }{ 2 } + \delta =0$ $\delta = -\frac{ \pi }{ 2 }$ $\arccos(x) + \arcsin(x) -\frac{ \pi }{ 2 }= 0$ Finally; $\arccos(x)= \frac{ \pi }{ 2 }- \arcsin(x)$

5. EmmaTassone

no problem ts not trouble xD

6. EmmaTassone

althought this demonstration is not general at all, if you look I choose arccos(0)=pi/2 but i could had chosen arccos(0)=3pi/2 ,5pi/2 , etc..

7. En

thanks :)))