Use the product-to-sum identities to express $2\cos\left(3x\right)\cos\left(9x\right)$2cos(3x)cos(9x) as a sum or difference of two trigonometric functions.
Express $\cos\left(3x+2y\right)\cos\left(x-y\right)$cos(3x+2y)cos(x−y) as a sum or difference of two trigonometric functions.
Evaluate $\cos105^\circ\cos15^\circ$cos105°cos15° by first expressing it as a sum or difference of two trigonometric functions using the product-to-sum identities.
Express $2\sin\left(3x\right)\sin\left(4x\right)$2sin(3x)sin(4x) as a sum or difference of two trigonometric functions by using the product-to-sum identities.