# `sec(arcsin(x - 1))` Write an algebraic expression that is equivalent to the given expression. (Hint: Sketch a right triangle.)

*print*Print*list*Cite

### 1 Answer

Taking (x-1) as oppsite side and 1 as the hypotenuse,the adjacent side will be equal to `sqrt(1-(x-1)^2)=sqrt(2x-x^2)`

`sin^-1(x-1)=sec^-1(1/(sqrt(2x-x^2)))`

`sec(sin^-1(x-1))=sec(sec^-1(1/(sqrt(2x-x^2))))`

`=1/(sqrt(2x-x^2))`