Question

follow these steps to derive the law of cosines.
$a^{2}=b^{2}-2bx+x^{2}+h^{2}$.

1. using the equation from step 1, the equation

$a^{2}=b^{2}-2bx+x^{2}+h^{2}$ becomes $a^{2}=b^{2}-2bx+c^{2}$
by substitution.

1. in $\triangle abd$, the trigonometric function $\cos(a)=\frac{x}{c}$.
2. multiply both sides of the equation in step 5 by $c$

to get $x = c \cos(a)$.

1. substitute for the variable $x$ in the equation

$a^{2}=b^{2}-2bx+c^{2}$ to produce $a^{2}=b^{2}-2bc \cos(a)+c^{2}$.
correct!
check

Explanation:

Step1: Identify substitution for x

From step 6, we derived $x = c \cos(A)$.

Step2: Substitute x into the equation

Replace $x$ with $c \cos(A)$ in $a^2 = b^2 - 2bx + c^2$.

Answer:

$c \cos(A)$