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In the following work, two reasons are not given (in steps 1 and 5). What are these reasons?
[math] vec{FC}^2 [/math]  [math] = [/math]  [math] FD^2 + CD^2[/math]  [math]"Step 1 "[/math] 
[math] [/math]  [math] = [/math]  [math] (vec{FE} + ED)^2 + CD^2[/math]  [math] "Info from previous questions"[/math] 
[math] [/math]  [math] = [/math]  [math] vec{FE}^2 + 2vec{FE} ED + ED^2 + CD^2 [/math]  [math] "Expanding the square"[/math] 
[math] [/math]  [math] = [/math]  [math] vec{FE}^2 + 2vec{FE} \ vec{EC}cos theta + vec{EC}^2 cos^2 theta + vec{EC}^2sin^2theta [/math]  [math]"Info from previous questions"[/math] 
[math] [/math]  [math] = [/math]  [math] vec{FE}^2 + 2vec{FE} \ vec{EC}cos theta + vec{EC}^2 [/math]  [math]"Step 5"[/math] 
[math] [/math]  [math] = [/math]  [math] vec{FE}^2 + vec{FB}^2 + 2vec{FE} \ vec{FB}cos theta [/math]  [math]"Info from previous questions"[/math] 
Taking the square root of both sides gives the formula for the magnitude of the sum of the vectors [math]vec{FB}[/math] and [math]vec{FE}[/math]:
[math] vec{FC} = sqrt(vec{FE}^2 + vec{FB}^2 + 2vec{FE} \ vec{FB}cos theta)[/math].

Pythagorean Theorem; [math]sin^2x + cos^2x = 1[/math]

Pythagorean Theorem; Law of Sines

Law of Vector Addition; Law of Cosines

Parallelogram Law; [math]cos2x = cos^2x  sin^2x[/math]