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

Problem

cos(2*x)=cos2(x)−sin2(x)

Solution

1. Identify the expression to be expanded using the cosine sum formula.

2. Rewrite the double angle 2*x as the sum of two identical angles x+x

cos(2*x)=cos(x+x)

3. Apply the formula for the cosine of a sum, which is cos(A+B)=cos(A)*cos(B)−sin(A)*sin(B)

cos(x+x)=cos(x)*cos(x)−sin(x)*sin(x)

4. Simplify the products of the trigonometric functions to reach the desired identity.

cos(x)*cos(x)−sin(x)*sin(x)=cos2(x)−sin2(x)

Final Answer

cos(2*x)=cos2(x)−sin2(x)

Want more problems? Check here!