Question

cos(cos^-1(x) + sin^-1(x)) rewrite as a algebraic expression

Answer 1

\[\cos (\cos ^{-1}x+\sin ^{-1}x)\]=\(\cos(\frac{ 1 }{ \cos x }+\frac{ 1 }{ \sin x })\)

=\(\cos (\frac{ \sin x + \cos x }{ \cos x \sin x })\)

can you do the remaining part?

Answer 2

So I'm not supposed to use the cos x+y identity

Answer 3

So is that the same as 1+ cotx?

Answer 4

@kryton1212

Answer 5

oh umm... i haven't learnt cotx yet. i am used to express it in simple theorem
@hartnn

Answer 6

well is that the same as 1+cot @kryton1212

Answer 7

cotx = 1/tanx
1+cotx=1+ 1/tanx

to continue my working steps, it equal to 1+1/tanx

so it's the same

Answer 8

they are the same*

Answer 9

arcsin x + arccos x = pi/2

Answer 10

o.0 i haven't learnt this haha you help him then :P

Answer 11

oops sorry

cos(cos^-1(x) + sin^-1(x))
=cos (pi/2)
=0

Answer 12

can you do a proof or explain why the sum of those two are equal to pi/2? @hartnn

Answer 13

its a standard relation,
but let me still prove it for you :)

Answer 14

sweet thank you!!!

Answer 15

i got the proof here
refer this,

http://mathforum.org/library/drmath/view/54161.html

if you have any doubts, do ask!