Question

prove the formula:
arccos x=1/2pi- arcsin x

please i still dont get it

Answer 1

do you know a bit of calculus?

Answer 2

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

Answer 3

sorry for the trouble :)

Answer 4

\[-\frac{ 1 }{ \sqrt{1-x²} }+\frac{ 1 }{ \sqrt {1-x²} }=0\]
\[\int\limits_{}^{}-\frac{ 1 }{ \sqrt{1-x²} } dx+\int\limits_{}^{}\frac{ 1 }{ \sqrt {1-x²} }dx=0\]
\[\arccos(x)+\arcsin(x)+\delta =0\]
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;
\[\arccos(x)= \frac{ \pi }{ 2 }- \arcsin(x)\]

Answer 5

no problem ts not trouble xD

Answer 6

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..

Answer 7

thanks :)))