Math

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the original problem was:
(sin x + cos x)^2 + (sin x - cos x)^2 = 2

steps too please

I got 1 for (sin x + cos x)^2

but then what does (sin x - cos x)^2 become since it's minus?

  • Math -

    see reply to your earlier post of this question

  • Math -

    (a+b)^2=a^2+2*a*b+b^2

    (a-b)^2=a^2-2*a*b+b^2

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

    [sin(x)-cos(x)]^2=
    [sin(x)]^2 -2*sin(x)*cos(x)+ [cos(x)]^2


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

    Becouse: [sin(x)]^2+[cos(x)]^2=1

  • Math -

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


    [sin(x)-cos(x)]^2=
    [sin(x)]^2 -2*sin(x)*cos(x)+ cos(x)]^2

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