write an algebraic expression which is equivalent to sin(arcsec(x+1))?

Question

Thanks guys

Answer 1

Let's work from the inside out.

y = arcsec(x + 1)
secy = x + 1
cosy = 1/secy = 1/(x + 1)

siny = √(1 - cos²y) = √[(1 - 1/(x + 1)²]

siny = √[(x + 1)² - 1] / (x + 1) = √(x² + 2x) / (x + 1)

Answer 2

Let y=arcsec(x+1)
sec(y)=x+1
cos(y)=1/(x+1)
sin(arcsec(x+1))=sin(y)
=sqrt(1-1/(x+1)^2)

Answer 3

x(x-1)/(x+1)

Answer 4

Well, we know that sine is the reciprocal of cosecant. So, if we move the expression to the bottom, we can make the outside term an cosecant.

1/[csc(arcsec(x+1))]