Lesson Worksheet: Angle Sum and Difference Trigonometric Identities Mathematics

In this worksheet, we will practice evaluating trigonometric expressions using the sum and difference of angle identities.


Simplify tantantantan33+299133299.

  • Atan266
  • Btantan33299
  • C233299tantan
  • Dtan332


Using the relation sinsincoscossin(𝛼𝛽)=𝛼𝛽𝛼𝛽, find an expression for sin(𝛼+𝛽).

  • Asinsincoscossin(𝛼+𝛽)=𝛼𝛽+𝛼𝛽
  • Bsinsincoscossin(𝛼+𝛽)=𝛼𝛽+𝛼𝛽
  • Csinsincoscossin(𝛼+𝛽)=𝛼𝛽𝛼𝛽
  • Dsinsincoscossin(𝛼+𝛽)=𝛼𝛽𝛼𝛽


Find the value of tan(𝐴𝐵) given sin𝐴=1517 and sin𝐵=45 where 𝐴 and 𝐵 are two positive acute angles.

  • A7736
  • B7736
  • C1384
  • D1112
  • E8413


In triangle 𝐴𝐵𝐶, 𝐴 and 𝐵 are acute angles, where sin𝐴=45, and cos𝐵=1213. Without using a calculator, find the value of cos𝐶.

  • A6516
  • B5665
  • C1665
  • D5665


Evaluate tantantantan112+23111223.

  • A3
  • B0
  • C1
  • D1


Given that sin𝐴=35 and cos𝐵=45, where 𝐴 and 𝐵 are two positive acute angles, determine cos(𝐴+𝐵).

  • A257
  • B725
  • C725
  • D1


Using the relations coscoscossinsin(𝛼𝛽)=𝛼𝛽+𝛼𝛽 and coscos(𝛼(𝛽))=(𝛼+𝛽), find an expression for cos(𝛼+𝛽).

  • Acossinsincoscos(𝛼+𝛽)=𝛼𝛽𝛼𝛽
  • Bcoscoscossinsin(𝛼+𝛽)=𝛼𝛽+𝛼𝛽
  • Ccoscoscossinsin(𝛼+𝛽)=𝛼𝛽𝛼𝛽
  • Dcoscoscossinsin(𝛼+𝛽)=𝛼𝛽𝛼𝛽


Does 𝐴+𝐵=45, given tan𝐴=1327 and tan𝐵=517?

  • AYes
  • BNo


Given that tan𝐴=724 and tan𝐵=34, where 𝐴 and 𝐵 are two positive acute angles, determine sin(𝐴+𝐵).

  • A44125
  • B44125
  • C54
  • D45


Find cot(𝐴+𝐵) given cos𝐴=725 and tan𝐵=43 where 𝐴 and 𝐵 are acute angles.

  • A34
  • B43
  • C100117
  • D100117
  • E43

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