Worksheet: Simplifying Trigonometric Expressions Using Trigonometric Identities

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

Q1:

Simplify sincoscsccot𝜃+𝜃𝜃𝜃.

  • Acos𝜃
  • B1
  • C𝜃cos
  • D1

Q2:

Simplify (1𝜃)+(1+𝜃)tantan.

  • A2𝜃csc
  • B2𝜃sec
  • Ccsc𝜃
  • Dsec𝜃

Q3:

Simplify 12𝑥1+2𝑥coscos.

  • Atan𝑥
  • Bcot2𝑥
  • Ctan2𝑥
  • Dcot𝑥

Q4:

Simplify 1+(90𝜃)cot.

  • Asec𝜃
  • Bcsc𝜃
  • Ctan𝜃
  • Dcot𝜃

Q5:

Simplify (1+𝜃)2𝜃cotcot.

  • Asec𝜃
  • Bcot𝜃
  • Ccsc𝜃
  • Dtan𝜃

Q6:

Simplify 1+𝜃1+𝜃tancot.

  • Acot𝜃
  • B1
  • Ctan𝜃
  • D1

Q7:

Simplify 1+𝜃1+𝜃cottan.

  • A1
  • Bcot𝜃
  • C1
  • Dtan𝜃

Q8:

Simplify 1+𝜃cot.

  • Acsc𝜃
  • B𝜃csc
  • Ccos𝜃
  • D𝜃cos

Q9:

Find the value of tancot(𝜋+𝐴)𝐴𝜋2 given 21𝐴=29csc where 3𝜋2<𝐴<2𝜋.

  • A2110
  • B41420
  • C41420
  • D2110

Q10:

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

  • A48143,48143
  • B574,574
  • C172,172
  • D2145,2145

Q11:

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

Q12:

Simplify 5𝑎𝑎sincot.

  • Acos2𝑎
  • B522𝑎cos
  • C522𝑎sin
  • Dsin2𝑎

Q13:

Simplify 𝑎𝑎cossin.

  • A122𝑎cos
  • Bcos2𝑎
  • C122𝑎sin
  • Dsin2𝑎

Q14:

Simplify 1𝜃𝜃𝜃sincsccot.

  • Asin𝜃
  • B𝜃cos
  • C𝜃sin
  • Dcos𝜃

Q15:

Simplify secsectan𝜃1𝜃𝜃.

  • Asin𝜃
  • B𝜃tan
  • C𝜃sin
  • Dtan𝜃

Q16:

Which of the following three identities are true?

  • Acoscossinsintantan(𝜃)=𝜃,(𝜃)=𝜃,(𝜃)=𝜃
  • Bcoscossinsintantan(𝜃)=𝜃,(𝜃)=𝜃,(𝜃)=𝜃
  • Ccoscossinsintantan(𝜃)=𝜃,(𝜃)=𝜃,(𝜃)=𝜃
  • Dcoscossinsintantan(𝜃)=𝜃,(𝜃)=𝜃,(𝜃)=𝜃
  • Ecoscossinsintantan(𝜃)=𝜃,(𝜃)=𝜃,(𝜃)=𝜃

Q17:

Which of the following is equivalent to 12𝜃sin?

  • A2𝜃sin
  • Bsin𝜃
  • C2𝜃cos
  • Dcos2𝜃
  • E22𝜃cos

Q18:

Which of the following expressions is equivalent to cossin𝜋4𝜋4?

  • A2𝜋4sin
  • Bcos𝜋4
  • C2𝜋4cos
  • Dcos𝜋2
  • Esin𝜋2

Q19:

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

  • Aan equation
  • Ban identity

Q20:

Which of the following is not a trigonometric identity?

  • Asinsin(𝜃)=𝜃
  • Bcos𝜃=12

Q21:

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

  • Acossin6𝑥6𝑥
  • B16𝑥sin
  • C26𝑥+16𝑥cossin
  • D26𝑥cos
  • E26𝑥6𝑥sincos

Q22:

Which of the following expressions is equal to sincoscossin𝜋2𝜃𝜃𝜋2𝜃(𝜋𝜃)?

  • A2𝜃𝜃sincos
  • B2𝜃cos
  • C22𝜃sin
  • Dcossin𝜃𝜃
  • E2𝜃sin

Q23:

Which of the following is a trigonometric identity?

  • A1+𝜃=𝜃tansec
  • Bcos𝜃=32

Q24:

Simplify cossec(360𝜃)(180+𝜃).

  • A𝜃sec
  • B1
  • C1
  • D𝜃cot

Q25:

Simplify coscsctantan𝜃(90𝜃)𝜃(90𝜃).

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