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

Problem

(cos(θ)−sin(θ))^2

Solution

1. Expand the square using the algebraic identity (a−b)^2=a^2−2*a*b+b^2

cos^2(θ)−2*cos(θ)*sin(θ)+sin^2(θ)

2. Rearrange the terms to group the squared trigonometric functions together.

sin^2(θ)+cos^2(θ)−2*sin(θ)*cos(θ)

3. Apply the Pythagorean identity sin^2(θ)+cos^2(θ)=1

1−2*sin(θ)*cos(θ)

4. Apply the double angle identity sin(2*θ)=2*sin(θ)*cos(θ) to simplify the expression further.

1−sin(2*θ)

Final Answer

(cos(θ)−sin(θ))^2=1−sin(2*θ)

Want more problems? Check here!