How do you verify ( 1 + sin x + cos x ) 2 = 2 ( 1 + sin x ) ( 1 + cos x ) ?

Answer 1

[ 1 + sin(x) + cos(x) ]² = [ 1 + sin(x) + cos(x) ] * [ 1 + sin(x) + cos(x) ] =

[ 1 + sin(x) + cos(x) ] + [ sin(x) + sin²(x) + sin(x) * cos(x) ] +

[ cos(x) + sin(x) * cos (x) + cos²(x) ] =

1 + sin²(x) + cos²(x) + 2 * sin(x) + 2 * cos(x) + 2 * sin(x) * cos(x) =

1 + 1 + 2 * sin(x) + 2 * cos(x) + 2 * sin(x) * cos(x) =

2 + 2 * sin(x) + 2 * cos(x) + 2 * sin(x) * cos(x) =

2 * [ 1 + sin(x) + cos(x) + sin(x) * cos(x) ] =

2 * [ 1 + sin(x) ] * [ 1 + cos(x) ]