Factor (sin(x)+cos(x))^2

Problem

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

Solution

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

sin^2(x)+2*sin(x)*cos(x)+cos^2(x)

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

sin^2(x)+cos^2(x)+2*sin(x)*cos(x)

3. Apply the Pythagorean identity sin^2(x)+cos^2(x)=1

1+2*sin(x)*cos(x)

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

1+sin(2*x)

Final Answer

(sin(x)+cos(x))^2=1+sin(2*x)

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