Question

follow these steps to derive the law of cosines.
✓ 2. the relationship between the side lengths in △cbd is
$a^{2}=(b - x)^{2}+h^{2}$ by the pythagorean theorem .
✓ 3. the equation $a^{2}=(b - x)^{2}+h^{2}$ is expanded to become
$a^{2}=b^{2}-2bx+x^{2}+h^{2}$.
✓ 4. 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 △abd, the trigonometric function $\heartsuit=\frac{x}{c}$.

correct!
check

Explanation:

Step1: Identify triangle sides

In right $\triangle ABD$, $x$ is adjacent to $\angle A$, $c$ is the hypotenuse.

Step2: Match trigonometric ratio

The cosine of an angle in a right triangle is $\frac{\text{adjacent}}{\text{hypotenuse}}$.
$\cos A = \frac{x}{c}$

Answer:

$\cos A$