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

Problem

cos(x)−sin(x)=1−2*sin(x)

Solution

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

cos(x)+sin(x)=1

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

cos(x)=1−sin(x)

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

(1−sin(x))−sin(x)

4. Combine the like terms to simplify the expression.

1−2*sin(x)

Final Answer

cos(x)−sin(x)=1−2*sin(x)

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