Simplify

Problem

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

Solution

1. Apply the difference of squares formula, (a−b)*(a+b)=a2−b2 to both the numerator and the denominator.

1−cos2(x)=1−cos2(x)

1−sin2(x)=1−sin2(x)

2. Substitute the Pythagorean identity sin2(x)+cos2(x)=1 into the expression.

1−cos2(x)=sin2(x)

1−sin2(x)=cos2(x)

3. Rewrite the fraction using the results from the previous step.

sin2(x)/cos2(x)

4. Apply the quotient identity tan(x)=sin(x)/cos(x) to simplify the expression further.

(sin(x)/cos(x))2=tan2(x)

Final Answer

((1−cos(x))*(1+cos(x)))/((1−sin(x))*(1+sin(x)))=tan2(x)

Want more problems? Check here!