Question

deriving the law of cosines
follow these steps to derive the law of cosines.

1. in △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).
3. substitute c cos(a) for the variable x in the equation a² = b² - 2bx + c² to produce a² = b² - 2bc cos(a) + c².
4. the law of cosines is obtained by the previous equation. a² = b² + c² - 2bc cos(a)

Explanation:

Step1: Analyze given steps

We have a series of steps related to triangle - trigonometry for deriving the law of cosines.

Step2: Identify the final operation

The equation $a^{2}=b^{2}-2bc\cos(A)+c^{2}$ can be rewritten as $a^{2}=b^{2}+c^{2}-2bc\cos(A)$ by re - arranging the terms. This is done through the commutative property of addition.

Answer:

re - arranging the terms