Factor by Grouping sin(x)^4-cos(x)^4

Problem

sin(x)−cos(x)

Solution

1. Identify the expression as a difference of squares, which follows the pattern a2−b2=(a−b)*(a+b)

2. Rewrite the terms as squares of squares to fit the pattern.

sin(x)−cos(x)=(sin(x))2−(cos(x))2

3. Apply the formula for the difference of squares using a=sin(x) and b=cos(x)

(sin(x)−cos(x))*(sin(x)+cos(x))

4. Identify the second factor as the Pythagorean identity, where sin(x)+cos(x)=1

(sin(x)−cos(x))*(1)

5. Factor again the first factor, which is also a difference of squares.

(sin(x)−cos(x))*(sin(x)+cos(x))

Final Answer

sin(x)−cos(x)=(sin(x)−cos(x))*(sin(x)+cos(x))

Want more problems? Check here!