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

Problem

(sin(x)−cos(x))2+sin(2*x)

Solution

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

sin2(x)−2*sin(x)*cos(x)+cos2(x)+sin(2*x)

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

sin2(x)−2*sin(x)*cos(x)+cos2(x)+2*sin(x)*cos(x)

3. Combine like terms to eliminate the 2*sin(x)*cos(x) terms.

sin2(x)+cos2(x)

4. Use the Pythagorean identity sin2(x)+cos2(x)=1 to find the final value.

1

Final Answer

(sin(x)−cos(x))2+sin(2*x)=1

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