Simplify cos(2theta)^2-sin(2theta)^2

Problem

cos(2*θ)−sin(2*θ)

Solution

1. Identify the expression as a specific form of a trigonometric identity. The expression follows the structure cos(A)−sin(A)

2. Apply the double-angle formula for cosine, which states cos(2*A)=cos(A)−sin(A)

3. Substitute A=2*θ into the identity to find the simplified form.

4. Simplify the resulting argument by multiplying the constants.

cos(2*(2*θ))=cos(4*θ)

Final Answer

cos(2*θ)−sin(2*θ)=cos(4*θ)

Want more problems? Check here!