Transformations of Products into sum or difference and vice versa

• The product-to-sum and sum-to-product identities can be used to transform products of trigonometric functions into sums or differences, and vice versa.
• The product-to-sum identity states that the product of two trigonometric functions can be expressed as the sum or difference of two other trigonometric functions.
• The sum-to-product identity states that the sum or difference of two trigonometric functions can be expressed as the product of two other trigonometric functions.
• The product-to-sum and sum-to-product identities are commonly used to simplify trigonometric expressions and solve trigonometric equations.
• The product-to-sum and sum-to-product identities can also be used to transform products or powers of trigonometric functions into sums or differences of trigonometric functions.

Important Formulas to Remember in these topic

---

• $\sin x\sin y=\frac{1}{2}[\cos(x-y)-\cos(x+y)]$
• $\cos x\cos y=\frac{1}{2}[\cos(x-y)+\cos(x+y)]$
• $\sin x\cos y=\frac{1}{2}[\sin(x+y)+\sin(x-y)]$
• $\tan x\pm\tan y=\frac{\sin(x\pm y)}{\cos x\cos y}$