### Home > PC3 > Chapter 8 > Lesson 8.1.3 > Problem8-47

8-47.

Given the equation $s^{2} + c^{2} = 1$, simplify each of the following expressions.

Rewrite the given equation in its various forms.
Substitute the appropriate expressions in each of the parts below.

$s^{2} = 1 − c^{2}$
$c^{2} = 1 − s^{2}$

1. $c^{2} + s^{2}$

1. $1-c^2$

1. $1-s^2$

1. $s + c$

1. $4\left(1-s^2\right)$

1. $4 – 4s^{2}$

Factor out a $4$ first. Then substitute an expression for $s^{2}$.