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

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