Simplify (sin(x)-cos(x))^2

Problem

(sin(x)−cos(x))2

Solution

1. Expand the square using the algebraic identity (a−b)2=a2−2*a*b+b2

sin2(x)−2*sin(x)*cos(x)+cos2(x)

2. Rearrange the terms to group the squared trigonometric functions together.

sin2(x)+cos2(x)−2*sin(x)*cos(x)

3. Apply the Pythagorean identity sin2(x)+cos2(x)=1

1−2*sin(x)*cos(x)

4. Apply the double angle identity sin(2*x)=2*sin(x)*cos(x) to further simplify the expression.

1−sin(2*x)

Final Answer

(sin(x)−cos(x))2=1−sin(2*x)

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