Lesson Worksheet: Product-to-Sum Identities Mathematics

In this worksheet, we will practice using the product-to-sum identity to simplify and evaluating trigonometric expression.


Simplify sincoscossin(𝑥+𝑦)𝑦(𝑥+𝑦)𝑦.

  • A2𝑥𝑦sincos
  • Bcos𝑥
  • C0
  • Dsin𝑥


Simplify coscos(𝐴𝐵)(𝐴+𝐵).

  • A0
  • B2𝐴𝐵coscos
  • C2𝐴𝐵sincos
  • D2𝐴𝐵sinsin


Simplify sinsin(𝐴+𝐵)(𝐴𝐵).

  • A0
  • B2𝐴𝐵sincos
  • C2𝐴𝐵sinsin
  • D2𝐴𝐵cossin


Write the expression 4(70)(33)coscos as a sum or difference of trigonometric expressions.

  • A2(37)+2(103)coscos
  • B2(103)2(37)coscos
  • C2103237sinsin
  • Dcoscos(37)+(103)
  • E237+2103sinsin


Find the exact value of 2(195)(45)cossin.

  • A1
  • B312
  • C13
  • D13
  • E132


Write the expression sinsin(80)+(20) as a product of trigonometric expressions.

  • Asinsin(50)(30)
  • B2(50)(30)sincos
  • Csincos(50)(30)
  • D2(50)(30)coscos
  • E2(50)(30)sinsin


Find the value of coscossinsin5𝑋𝑋+5𝑋𝑋 given sin2𝑋=38.

  • A2332
  • B4132
  • C7364
  • D5564


Find cos(2𝑎+𝑏) given 4𝑎=3tan and 3𝑏=4tan where 𝑎 and 𝑏 are acute angles.

  • A0
  • B35
  • C117125
  • D310


The intensity of an electric current is given by 𝐶=52(75𝑡)sin where 𝑡 is the time in seconds. Find the intensity after one second without using a calculator using sum and product formulae.

  • A562
  • B5628
  • C56+2
  • D56+28


Find the value of sinsinsinsinsinsin𝜋12+3𝜋12+5𝜋12+7𝜋12+9𝜋12+11𝜋12.

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