Simplify cos(u+v)cos(v)+sin(u+v)sin(v)

Problem

cos(u+v)*cos(v)+sin(u+v)*sin(v)

Solution

1. Identify the trigonometric identity for the cosine of a difference, which states cos(A−B)=cos(A)*cos(B)+sin(A)*sin(B)

2. Match the components of the given expression to the identity by letting A=u+v and B=v

3. Substitute these values into the identity to rewrite the expression as a single cosine function.

4. Simplify the argument of the cosine function by subtracting the terms.

u+v−v=u

Final Answer

cos(u+v)*cos(v)+sin(u+v)*sin(v)=cos(u)

Want more problems? Check here!