Verify the Identity cos(x)^2-sin(x)^2=2cos(x)^2-1

Problem

cos(x)−sin(x)=2*cos(x)−1

Solution

1. Identify the Pythagorean identity that relates sin(x) and cos(x)

sin(x)+cos(x)=1

2. Rearrange the identity to solve for sin(x) in terms of cos(x)

sin(x)=1−cos(x)

3. Substitute the expression for sin(x) into the left side of the original equation.

cos(x)−(1−cos(x))

4. Distribute the negative sign through the parentheses.

cos(x)−1+cos(x)

5. Combine the like terms to simplify the expression.

2*cos(x)−1

Final Answer

cos(x)−sin(x)=2*cos(x)−1

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