Simplify ((sin(x)+cos(x))^2)/(1+2sin(x)cos(x))

Problem

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

Solution

1. Expand the numerator using the square of a binomial formula (a+b)^2=a^2+2*a*b+b^2

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

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

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

3. Simplify the fraction by dividing the numerator by the identical denominator.

1

Final Answer

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

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