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Worksheet: Angle Sum and Difference Identities

Q1:

Simplify t a n t a n t a n t a n ( 1 1 8 βˆ’ 2 𝑋 ) + ( 3 2 + 2 𝑋 ) 1 βˆ’ ( 1 1 8 βˆ’ 2 𝑋 ) ( 3 2 + 2 𝑋 ) ∘ ∘ ∘ ∘ .

  • A √ 3 3
  • B βˆ’ √ 3
  • C √ 3
  • D βˆ’ √ 3 3

Q2:

Simplify s i n c o s c o s s i n ( 2 6 6 + 8 𝑋 ) ( 9 4 βˆ’ 8 𝑋 ) + ( 2 6 6 + 8 𝑋 ) ( 9 4 βˆ’ 8 𝑋 ) ∘ ∘ ∘ ∘ .

  • A βˆ’ 1 2
  • B1
  • C βˆ’ 1
  • D0

Q3:

Evaluate t a n t a n t a n t a n 7 9 βˆ’ 1 2 4 1 + 7 9 1 2 4 ∘ ∘ ∘ ∘ .

  • A0
  • B1
  • C √ 3
  • D βˆ’ 1

Q4:

Which of the following is equivalent to t a n 2 1 5 ∘ ?

  • A 1 + 1 0 1 βˆ’ 1 0 t a n t a n ∘ ∘
  • B t a n t a n 1 0 βˆ’ 1 1 0 + 1 ∘ ∘
  • C t a n t a n 1 0 + 1 1 0 βˆ’ 1 ∘ ∘
  • D 1 βˆ’ 1 0 1 + 1 0 t a n t a n ∘ ∘

Q5:

Find the value of s i n c o s c o s s i n ο€Ό 2 πœ‹ 3  ο€» πœ‹ 2  βˆ’ ο€Ό 2 πœ‹ 3  ο€» πœ‹ 2  .

  • A √ 3 2
  • B βˆ’ 1 2
  • C βˆ’ √ 3 2
  • D 1 2

Q6:

Find the value of s i n c o s c o s s i n ο€» πœ‹ 2  ο€» πœ‹ 3  βˆ’ ο€» πœ‹ 2  ο€» πœ‹ 3  .

  • A √ 3 2
  • B βˆ’ 1 2
  • C βˆ’ √ 3 2
  • D 1 2

Q7:

Does 𝐴 + 𝐡 = 4 5 ∘ , given t a n 𝐴 = 1 3 2 7 and t a n 𝐡 = 5 1 7 ?

  • Ano
  • Byes

Q8:

Evaluate s i n c o s c o s s i n ο€» πœ‹ 3  ο€» πœ‹ 3  + ο€» πœ‹ 3  ο€» πœ‹ 3  .

  • A 1 2
  • B βˆ’ 1 2
  • C βˆ’ √ 3 2
  • D √ 3 2

Q9:

Evaluate s i n c o s c o s s i n ο€Ό 7 πœ‹ 1 2  ο€» πœ‹ 3  βˆ’ ο€Ό 7 πœ‹ 1 2  ο€» πœ‹ 3  .

  • A √ 3 2
  • B βˆ’ √ 2 2
  • C βˆ’ √ 3 2
  • D √ 2 2

Q10:

Evaluate s i n c o s c o s s i n ο€Ό 2 πœ‹ 3  ο€» πœ‹ 6  βˆ’ ο€Ό 2 πœ‹ 3  ο€» πœ‹ 6  .

  • A βˆ’ 1
  • B βˆ’ 1 2
  • C0
  • D1

Q11:

Evaluate t a n t a n t a n t a n 1 1 2 + 2 3 1 βˆ’ 1 1 2 2 3 ∘ ∘ ∘ ∘ .

  • A0
  • B1
  • C √ 3
  • D βˆ’ 1

Q12:

Find the value of s i n c o s c o s s i n s i n c o s c o s s i n ( 1 6 ) ( 4 4 ) + ( 1 6 ) ( 4 4 ) ( 2 2 ) ( 3 8 ) + ( 2 2 ) ( 3 8 ) ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ without using a calculator.

  • A0
  • B 1 2
  • C √ 3 2
  • D1

Q13:

Find the value of s i n c o s c o s s i n s i n c o s c o s s i n ( 2 6 ) ( 3 4 ) + ( 2 6 ) ( 3 4 ) ( 1 1 ) ( 1 9 ) + ( 1 1 ) ( 1 9 ) ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ without using a calculator.

  • A √ 3 3
  • B 1 2
  • C √ 3 2
  • D √ 3

Q14:

Evaluate s i n c o s c o s s i n ο€Ό π‘₯ + 1 1 πœ‹ 6  ο€Ό π‘₯ + 4 πœ‹ 3  βˆ’ ο€Ό π‘₯ + 1 1 πœ‹ 6  ο€Ό π‘₯ + 4 πœ‹ 3  .

  • A βˆ’ 1
  • B βˆ’ 1 2
  • C0
  • D1

Q15:

, and are three angles of a triangle where and . Does ?

  • Ano
  • Byes

Q16:

Evaluate s i n c o s s i n c o s 7 4 2 9 βˆ’ 1 6 6 1 ∘ ∘ ∘ ∘ without using a calculator.

  • A βˆ’ √ 2 2
  • B √ 3 2
  • C βˆ’ √ 3 2
  • D √ 2 2

Q17:

Evaluate s i n c o s s i n c o s 7 5 3 0 βˆ’ 1 5 6 0 ∘ ∘ ∘ ∘ without using a calculator.

  • A βˆ’ √ 2 2
  • B √ 3 2
  • C βˆ’ √ 3 2
  • D √ 2 2

Q18:

The intensity of an electric current is given by 𝐢 = 1 1 2 ( 1 0 5 𝑑 ) s i n ∘ where 𝑑 is the time in seconds. Rewrite the intensity after one second using sum and product formulae in terms of special angles.

  • A 1 1 2 ( 4 5 6 0 βˆ’ 4 5 6 0 ) c o s c o s c o s c o s ∘ ∘ ∘ ∘
  • B 1 1 2 ( 4 5 6 0 βˆ’ 4 5 6 0 ) s i n c o s c o s s i n ∘ ∘ ∘ ∘
  • C 1 1 2 ( 4 5 6 0 + 4 5 6 0 ) s i n c o s c o s c o s ∘ ∘ ∘ ∘
  • D 1 1 2 ( 4 5 6 0 + 4 5 6 0 ) s i n c o s c o s s i n ∘ ∘ ∘ ∘

Q19:

Find t a n 2 8 5 ∘ .

  • A βˆ’ 2 + √ 3
  • B 2 + √ 3
  • C 2 βˆ’ √ 3
  • D βˆ’ 2 βˆ’ √ 3

Q20:

Find t a n πœƒ given t a n ( πœƒ + 4 5 ) = 5 2 4 ∘ .

  • A βˆ’ 2 9 1 9
  • B 1 9 2 9
  • C 2 4 5
  • D βˆ’ 1 9 2 9

Q21:

Find π‘Ž given s i n c o s c o s s i n 4 4 2 3 = π‘Ž βˆ’ 4 4 2 3 ∘ ∘ ∘ ∘ .

  • A c o s 2 1 ∘
  • B s i n 2 1 ∘
  • C c o s 6 7 ∘
  • D s i n 6 7 ∘

Q22:

Find t a n ( πœƒ + 4 5 ) ∘ given t a n πœƒ = βˆ’ 3 7 .

  • A βˆ’ 7 3
  • B 3 7
  • C 5 2
  • D 2 5