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Maths problem: arcsinx - arccosx = pi/2 watch

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1. Can someone point out what is wrong with this proof?

y = cos(x)
arccos(y) = x

sin(arccos(y) + pi/2 ) = cos(arccos(y)) -because sin(x+pi/2) = cos(x)

sin(arccos(y) + pi/2 ) = y

arccos(y) + pi/2 = arcsin(y)

arcsin(y)-arccos(y) = pi/2
2. (Original post by BeyondDoubt)
Can someone point out what is wrong with this proof?

y = cos(x)
arccos(y) = x

sin(arccos(y) + pi/2 ) = cos(arccos(y)) -because sin(x+pi/2) = cos(x)

sin(arccos(y) + pi/2 ) = y

arccos(y) + pi/2 = arcsin(y)

arcsin(y)-arccos(x) = pi/2
the x should be a y ^^^
3. (Original post by BeyondDoubt)
sin(arccos(y) + pi/2 ) = y

arccos(y) + pi/2 = arcsin(y)
Here

holds only in the interval , and has a range of . If you instead use , which has a range of , you will get the correct result.
4. (Original post by _gcx)
Here

holds only in the interval , and has a range of . If you instead use , which has a range of , you will get the correct result.
Thank you!

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