Simplify 1-cos(x)^2

Problem

1−cos2(x)

Solution

1. Identify the expression as a component of the fundamental Pythagorean identity in trigonometry.

2. Recall the Pythagorean identity, which states that for any angle x the sum of the squares of sine and cosine is equal to 1.

sin2(x)+cos2(x)=1

3. Rearrange the identity to isolate the term that matches the given expression by subtracting cos2(x) from both sides of the equation.

sin2(x)=1−cos2(x)

Final Answer

1−cos2(x)=sin2(x)

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