Lesson Worksheet: Simplifying Trigonometric Expressions Using Trigonometric Identities Mathematics

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 1+(90𝜃)cot.

  • Asec𝜃
  • Bcsc𝜃
  • Ctan𝜃
  • Dcot𝜃

Q4:

Simplify (1+𝜃)2𝜃cotcot.

  • Asec𝜃
  • Bcot𝜃
  • Ccsc𝜃
  • Dtan𝜃

Q5:

Simplify 1+𝜃1+𝜃tancot.

  • Acot𝜃
  • B1
  • Ctan𝜃
  • D1

Q6:

Simplify 1+𝜃1+𝜃cottan.

  • A1
  • Bcot𝜃
  • C1
  • Dtan𝜃

Q7:

Simplify 1+𝜃cot.

  • Acsc𝜃
  • B𝜃csc
  • Ccos𝜃
  • D𝜃cos

Q8:

Simplify 1𝜃𝜃𝜃sincsccot.

  • Asin𝜃
  • B𝜃cos
  • C𝜃sin
  • Dcos𝜃

Q9:

Simplify secsectan𝜃1𝜃𝜃.

  • Asin𝜃
  • B𝜃tan
  • C𝜃sin
  • Dtan𝜃

Q10:

Which of the following expressions is equivalent to cossin𝜋4𝜋4?

  • A2𝜋4sin
  • Bcos𝜋4
  • C2𝜋4cos
  • Dcos𝜋2
  • Esin𝜋2

Q11:

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

  • Aan equation
  • Ban identity

Q12:

Which of the following is not a trigonometric identity?

  • Asinsin(𝜃)=𝜃
  • Bcos𝜃=12

Q13:

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

  • A2𝜃𝜃sincos
  • B2𝜃cos
  • C22𝜃sin
  • Dcossin𝜃𝜃
  • E2𝜃sin

Q14:

Which of the following is a trigonometric identity?

  • A1+𝜃=𝜃tansec
  • Bcos𝜃=32

Q15:

Simplify cossec(360𝜃)(180+𝜃).

  • A𝜃sec
  • B1
  • C1
  • D𝜃cot

Q16:

Simplify coscsctantan𝜃(90𝜃)𝜃(90𝜃).

Q17:

Simplify 1𝜃1𝜃coscot in its simplest form.

Q18:

Simplify 2𝜃+𝜃+1𝜃sincossec.

Q19:

Simplify 1𝜃1𝜃sintan.

Q20:

Simplify cot(180𝜃).

  • Acot𝜃
  • Btan𝜃
  • C𝜃cot
  • D𝜃tan

Q21:

Consider the identity sincos𝜃+𝜃=1. We can use this to derive two new identities.

First, divide both sides of the identity by sin𝜃 to find an identity in terms of cot𝜃 and cosec𝜃.

  • A1+𝜃=𝜃cotsec
  • B1+𝜃=𝜃cotcosec
  • C1+𝜃=𝜃tancosec
  • D1+𝜃=𝜃tansin
  • E1+𝜃=𝜃cotsin

Now, divide both sides of the identity through by cos𝜃 to find an identity in terms of tan𝜃 and sec𝜃.

  • Acotsec𝜃+1=𝜃
  • Btancos𝜃+1=𝜃
  • Ctancosec𝜃+1=𝜃
  • Dtansec𝜃+1=𝜃
  • Etansin𝜃+1=𝜃

Q22:

The figure shows a unit circle and a radius with the lengths of its 𝑥- and 𝑦-components. Use the Pythagorean theorem to derive an identity connecting the lengths 1, cos𝜃, and sin𝜃.

  • Asincos𝜃+𝜃=1
  • Bsincos𝜃𝜃=1
  • C1+𝜃=𝜃cossin
  • Dsincos𝜃+𝜃=1
  • E1+𝜃=𝜃cossin

Q23:

For any 𝑥𝑘𝜋(𝑘), what is 1+𝑥cot?

  • Acos𝑥
  • Bsin𝑥
  • C1𝑥cos
  • D1𝑥sin
  • E1𝑥sin

Q24:

For any 𝑥𝜋2+𝑘𝜋(𝑘), what is cos𝑥?

  • A1𝑥tan
  • B1+𝑥tan
  • C11+𝑥cot
  • D1+𝑥cot
  • E11+𝑥tan

Q25:

For any 𝑥0+𝑘𝜋(𝑘), what is sin𝑥?

  • A11+𝑥cot
  • B11+𝑥tan
  • C1+𝑥tan
  • D1+𝑥cot
  • E1𝑥cot

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