Worksheet: Simplifying Trigonometric Expressions Using Trigonometric Identities

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In this worksheet, we will practice simplifying trigonometric expressions by applying trigonometric identities.

Q1:

Simplify sincoscsccot𝜃+𝜃𝜃−𝜃.

  • A c o s 𝜃
  • B − 1
  • C − 𝜃 c o s
  • D1

Q2:

Simplify (1−𝜃)+(1+𝜃)tantan.

  • A 2 𝜃 c s c
  • B 2 𝜃 s e c
  • C c s c 𝜃
  • D s e c 𝜃

Q3:

Simplify 1−2𝑥1+2𝑥coscos.

  • A t a n 𝑥
  • B c o t 2 𝑥
  • C t a n 2 𝑥
  • D c o t 𝑥

Q4:

Simplify 1+(90−𝜃)cot∘.

  • A s e c 𝜃
  • B c s c 𝜃
  • C t a n 𝜃
  • D c o t 𝜃

Q5:

Simplify (1+𝜃)−2𝜃cotcot.

  • A s e c 𝜃
  • B c o t 𝜃
  • C c s c 𝜃
  • D t a n 𝜃

Q6:

Simplify 1+𝜃1+𝜃tancot.

  • A c o t 𝜃
  • B − 1
  • C t a n 𝜃
  • D1

Q7:

Simplify 1+−𝜃1+−𝜃cottan.

  • A − 1
  • B c o t 𝜃
  • C1
  • D t a n 𝜃

Q8:

Simplify 1+𝜃cot.

  • A c s c 𝜃
  • B − 𝜃 c s c
  • C c o s 𝜃
  • D − 𝜃 c o s

Q9:

Find the value of tancot(𝜋+𝐴)−𝐴−𝜋2 given 21𝐴=−29csc where 3𝜋2<𝐴<2𝜋.

  • A − 2 1 1 0
  • B − 4 1 4 2 0
  • C 4 1 4 2 0
  • D 2 1 1 0

Q10:

Find the possible values of tancot𝜃−𝜃 given that tancot𝜃+𝜃=24.

  • A 4 8 √ 1 4 3 , − 4 8 √ 1 4 3
  • B √ 5 7 4 , − √ 5 7 4
  • C 1 7 √ 2 , − 1 7 √ 2
  • D 2 √ 1 4 5 , − 2 √ 1 4 5

Q11:

Find the value of tancot𝜃+𝜃 given tancot𝜃+𝜃=6.

Q12:

Simplify 5𝑎𝑎sincot.

  • A c o s 2 𝑎
  • B 5 2 2 𝑎 c o s
  • C 5 2 2 𝑎 s i n
  • D s i n 2 𝑎

Q13:

Simplify √𝑎𝑎cossin.

  • A 1 2 2 𝑎 c o s
  • B c o s 2 𝑎
  • C 1 2 2 𝑎 s i n
  • D s i n 2 𝑎

Q14:

Simplify 1−𝜃𝜃−𝜃sincsccot.

  • A s i n 𝜃
  • B − 𝜃 c o s
  • C − 𝜃 s i n
  • D c o s 𝜃

Q15:

Simplify secsectan𝜃−1𝜃−𝜃.

  • A s i n 𝜃
  • B − 𝜃 t a n
  • C − 𝜃 s i n
  • D t a n 𝜃

Q16:

Which of the following three identities are true?

  • A c o s c o s s i n s i n t a n t a n ( − 𝜃 ) = − 𝜃 , ( − 𝜃 ) = 𝜃 , ( − 𝜃 ) = − 𝜃
  • B c o s c o s s i n s i n t a n t a n ( − 𝜃 ) = 𝜃 , ( − 𝜃 ) = 𝜃 , ( − 𝜃 ) = 𝜃
  • C c o s c o s s i n s i n t a n t a n ( − 𝜃 ) = − 𝜃 , ( − 𝜃 ) = − 𝜃 , ( − 𝜃 ) = 𝜃
  • D c o s c o s s i n s i n t a n t a n ( − 𝜃 ) = 𝜃 , ( − 𝜃 ) = − 𝜃 , ( − 𝜃 ) = − 𝜃
  • E c o s c o s s i n s i n t a n t a n ( − 𝜃 ) = − 𝜃 , ( − 𝜃 ) = − 𝜃 , ( − 𝜃 ) = − 𝜃

Q17:

Which of the following is equivalent to 1−2𝜃sin∘?

  • A − 2 𝜃 s i n ∘
  • B s i n 𝜃 ∘
  • C − 2 𝜃 c o s ∘
  • D c o s 2 𝜃 ∘
  • E 2 2 𝜃 c o s ∘

Q18:

Which of the following expressions is equivalent to cossin𝜋4−𝜋4?

  • A 2 𝜋 4 s i n
  • B c o s 𝜋 4
  • C 2 𝜋 4 c o s
  • D c o s 𝜋 2
  • E s i n 𝜋 2

Q19:

Is 1+𝜃=𝜃tansec an identity or an equation?

  • Aan equation
  • Ban identity

Q20:

Which of the following is not a trigonometric identity?

  • A s i n s i n ( − 𝜃 ) = − 𝜃
  • B c o s 𝜃 = 1 2

Q21:

Which of the following expressions is equivalent to cossin12𝑥+6𝑥?

  • A c o s s i n 6 𝑥 − 6 𝑥
  • B 1 − 6 𝑥 s i n
  • C 2 6 𝑥 + 1 − 6 𝑥 c o s s i n
  • D 2 6 𝑥 c o s
  • E 2 6 𝑥 6 𝑥 s i n c o s

Q22:

Which of the following expressions is equal to sincoscossin𝜋2−𝜃𝜃−𝜋2−𝜃(𝜋−𝜃)?

  • A 2 𝜃 𝜃 s i n c o s
  • B 2 𝜃 c o s
  • C 2 2 𝜃 s i n
  • D c o s s i n 𝜃 − 𝜃
  • E 2 𝜃 s i n

Q23:

Which of the following is a trigonometric identity?

  • A 1 + 𝜃 = 𝜃 t a n s e c
  • B c o s 𝜃 = √ 3 2

Q24:

Simplify cossec(360−𝜃)(180+𝜃)∘∘.

  • A − 𝜃 s e c
  • B − 1
  • C1
  • D − 𝜃 c o t

Q25:

Simplify coscsctantan𝜃(90−𝜃)−𝜃(90−𝜃)∘∘.

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