Question

The difference formula for cosine is$\cos \left(A-B\right)=\_\_\_\_\_\_\_\_.$

Short answer

The difference formula for cosine is$\cos \left(A-B\right)=\mathit{c}\mathit{o}\mathit{s}\mathit{A}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{B}\mathbf{}\mathbf{+}\mathbf{}\mathit{s}\mathit{i}\mathit{n}\mathit{A}\mathbf{}\mathit{s}\mathit{i}\mathit{n}\mathit{B}.$

Step-by-step solution

Step 1. Given Information

The cosine function is a periodic function. The difference formula for cosine states that the product of the cosines of the angles plus the product of the sine of the angles is equal to the difference of the cosine of the two angles.

Step 2. Filling the blank

The difference formula for cosine is$\cos \left(A-B\right)=\cos A\cos B+\sin A\sin B.$