What is the value of (sin x - cos x)^2 + (sin x + cos x)^2 for x = 30 and for x = 60 degrees.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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First, look at the expression that you have to evaluate for the different values of x.

It is possible to simplify `(sin x - cos x)^2 + (sin x + cos x)^2` as follows:

`(sin x - cos x)^2 + (sin x + cos x)^2`

Use the fact `(a - b)^2 = a^2 + b^2 - 2ab` and `(a+b)^2 = a^2+b^2 +2ab`

= `sin^2 x + cos^2x - 2*cos x*sin x + sin^2 x + cos^2x + 2*cos x*sin x`

Use the identity `sin^2x + cos^2x = 1`

= `1 - 2*cos x*sin x + 1 + 2*cos x*sin x`

= 2

The value of the expression `(sin x - cos x)^2 + (sin x + cos x)^2` is a constant and irrespective of the value of x, the expression is equal to 2

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