Lesson Worksheet: Simplifying Trigonometric Expressions Using Trigonometric Identities Mathematics • 10th Grade

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

Q1:

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
  • Bsincos𝜃−𝜃=1
  • C1+𝜃=𝜃cossin
  • Dsincos𝜃+𝜃=1
  • E1+𝜃=𝜃cossin

Q2:

Simplify sincsccos𝜃𝜃−𝜃.

  • Acsc𝜃
  • Btan𝜃
  • Csin𝜃
  • Dsec𝜃

Q3:

Simplify (𝜃+𝜃)−2𝜃𝜃sincossincos.

Q4:

Simplify 1𝜃−1𝜃sintan.

Q5:

Simplify (1−𝜃)+(1+𝜃)tantan.

  • A2𝜃csc
  • B2𝜃sec
  • Ccsc𝜃
  • Dsec𝜃

Q6:

Simplify 31𝜃+26𝜃sincos.

  • A26+5𝜃cos
  • B57+𝜃cos
  • C57+𝜃sin
  • D26+5𝜃sin

Q7:

Simplify 1+−𝜃1+−𝜃cottan.

  • A−1
  • Bcot𝜃
  • C1
  • Dtan𝜃

Q8:

Simplify sinsin∘∘(180−𝜃)+(270−𝜃).

Q9:

Simplify sincoscsccot𝜃+𝜃𝜃−𝜃.

  • Acos𝜃
  • B−1
  • C−𝜃cos
  • D1

Q10:

Simplify sincossincos𝜃−𝜃𝜃−𝜃.

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