Question

rewrite the expression as an algebraic expression in x

sin(2sin^-1(2x))

Answer 1

Welcome to OpenStudy @secnorc what exactly are you having trouble on? Do you understand how to do this or not at all/

Answer 2

I've solved some like cos(tan^-1(3x)), but this one I am not getting

Answer 3

Are you able to walk me throught it?

Answer 4

use these identitties :
sin(2x) = 2sin(x)cos(x) and
sin^2 (x) + cos^2 (x) = 1

Answer 5

I'm still not understanding where to go

Answer 6

sin(2sin^-1(2x)), in parantheses is double angles right ?
so, it can rewitten as :
sin(2sin^-1(2x)) = 2 sin(sin^-1(2x)) cos sin(sin^-1(2x)), agree ?

Answer 7

okay, yes

Answer 8

2 sin(sin^-1(2x)) cos sin(sin^-1(2x))
lets do slowly ;)
obvious, for sin(sin^-1(2x)) = 2x, right ?

Answer 9

Right

Answer 10

ok, we get
2 sin(sin^-1(2x)) cos sin(sin^-1(2x))
= 2 (2x) cos sin(sin^-1(2x))
= (4x) cos sin(sin^-1(2x))

now, still be a problem for cos sin(sin^-1(2x)), right ?

Answer 11

yeah, would it come out being (4x)cos(2x) next?

Answer 12

oppps,, typo there that should like this :
2 sin(sin^-1(2x)) cos(sin^-1(2x))
= 2 (2x) cos(sin^-1(2x))
= 4x cos(sin^-1(2x))

now the problem is for evaluate the cos(sin^-1(2x))

Answer 13

is it sqrt(4x^2+1)/1?

Answer 14

let's check together :)

see this identity :
sin^2 (x) + cos^2 (x) = 1
cos^2 (x) = 1 - sin^2 (x)
cos(x) = sqrt (1 - sin^2 (x))

now for evaluate cos(sin^-1(2x)), it can be
cos(sin^-1(2x)) = sqrt (1 - sin^2 (sin^-1(2x)) )
= sqrt (1 - (2x)^2 )
= sqrt(1 - 4x^2)

Answer 15

(4x)sqrt(1-4x^2)

Answer 16

yes, totally is right

Answer 17

Thank you so much!!

Answer 18

you're welcome ;)