Question

deriving the law of cosines
follow these steps to derive the law of cosines.
a² = b² - 2bx + x²+h².
√4. using the equation from step 1, the equation
a² = b² - 2bx + x² + h² becomes a² = b² - 2bx + c²
by substitution.
√5. in △abd, the trigonometric function cos(a) = (\frac{x}{c}).
√6. 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

a² = b² - 2bx + c² to produce a² = b² - 2bc cos(a)+c².

Explanation:

Step1: Recall previous result

We have the equation $a^{2}=b^{2}-2bx + c^{2}$.

Step2: Recall cosine - relation

From step 5, we know $x = c\cos(A)$.

Step3: Substitute $x$ value

Substitute $x = c\cos(A)$ into $a^{2}=b^{2}-2bx + c^{2}$. So $a^{2}=b^{2}-2b(c\cos(A))+c^{2}=b^{2}-2bc\cos(A)+c^{2}$.

Answer:

$c\cos(A)$