Question

Show that \(\sin^{-1}(x) + \cos^{-1}(x) = \dfrac{\pi}{2}\) for \(|x| \leq 1\)

Answer 1

What identifies would be great for me to use?

I just need me some leads...

Answer 2

derivative? it would get me to 0 = 0.

ok so I know arcsin(x) + arccos(x) should be equal to constant, but why pi/2 ?

Answer 3

@Loser66

Answer 4

I don't know, but why not pi/2? it's a number, still

Answer 5

we can't just make up what it equal to, that's not really math lol...

Answer 6

x+y=pi/2
y=pi/2-x

Put sin x=k
sin y=l

sin^-1 k+sin^-1 l=x+pi/2-x=pi/2

Answer 7

Is that explanation convincing? :)

Answer 8

hmm yeah. good enough lol.

thanks! I was just curious.

Answer 9

yw :)