# [SOLVED] Simplification

• Feb 19th 2010, 08:54 PM
Dotdash13
[SOLVED] Simplification
I need help understanding the question: simplify the expression $\displaystyle cos^2(arcsin t)$ using the property that inverses "undo" each other.
I get that $\displaystyle arcsin(t)=sin^-1(t)$ and that that would be the opposite of $\displaystyle sin(t)$. But $\displaystyle cos(t)$ isn't the opposite of $\displaystyle sin(t)$, is it?
Yes, I do know what simplifying is, but I'm not sure how to do it here.
• Feb 19th 2010, 08:57 PM
Prove It
Quote:

Originally Posted by Dotdash13
I need help understanding the question: simplify the expression $\displaystyle cos^2(arcsin t)$ using the property that inverses "undo" each other.
I get that $\displaystyle arcsin(t)=sin^-1(t)$ and that that would be the opposite of $\displaystyle sin(t)$. But $\displaystyle cos(t)$ isn't the opposite of $\displaystyle sin(t)$, is it?
Yes, I do know what simplifying is, but I'm not sure how to do it here.

$\displaystyle \cos^2{x} + \sin^2{x} = 1$ so $\displaystyle \cos^2{x} = 1 - \sin^2{x}$.

Therefore $\displaystyle \cos^2{\arcsin{t}} = 1 - \sin^2{\arcsin{t}} = 1 - t^2$.