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

Problem

(sin(a)−cos(a))2

Solution

1. Expand the square using the algebraic identity (x−y)2=x2−2*x*y+y2

(sin(a)−cos(a))2=sin2(a)−2*sin(a)*cos(a)+cos2(a)

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

sin2(a)+cos2(a)−2*sin(a)*cos(a)

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

1−2*sin(a)*cos(a)

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

1−sin(2*a)

Final Answer

(sin(a)−cos(a))2=1−sin(2*a)

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