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

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 π‘₯- and 𝑦-components. Use the Pythagorean theorem to derive an identity connecting the lengths 1, cosπœƒ, and sinπœƒ.

  • Asincosπœƒ+πœƒ=1
  • BsincosοŠ¨οŠ¨πœƒβˆ’πœƒ=1
  • C1+πœƒ=πœƒcossin
  • DsincosοŠ¨οŠ¨πœƒ+πœƒ=1
  • E1+πœƒ=πœƒcossin

Q2:

Simplify sincsccosπœƒπœƒβˆ’πœƒοŠ¨.

  • AcscοŠ¨πœƒ
  • BtanοŠ¨πœƒ
  • CsinοŠ¨πœƒ
  • DsecοŠ¨πœƒ

Q3:

Simplify (πœƒ+πœƒ)βˆ’2πœƒπœƒsincossincos.

Q4:

Simplify 1πœƒβˆ’1πœƒsintan.

Q5:

Simplify (1βˆ’πœƒ)+(1+πœƒ)tantan.

  • A2πœƒcsc
  • B2πœƒsec
  • CcscοŠ¨πœƒ
  • DsecοŠ¨πœƒ

Q6:

Simplify 31πœƒ+26πœƒsincos.

  • A26+5πœƒcos
  • B57+πœƒcos
  • C57+πœƒsin
  • D26+5πœƒsin

Q7:

Simplify 1+ο€»βˆ’πœƒο‡1+ο€»βˆ’πœƒο‡cottanοŠ¨οŠ©οŽ„οŠ¨οŠ¨οŽ„οŠ¨.

  • Aβˆ’1
  • BcotοŠ¨πœƒ
  • C1
  • DtanοŠ¨πœƒ

Q8:

Simplify sinsin∘∘(180βˆ’πœƒ)+(270βˆ’πœƒ).

Q9:

Simplify sincoscsccotοŠ¨οŠ¨οŠ¨οŠ¨πœƒ+πœƒπœƒβˆ’πœƒ.

  • AcosοŠ¨πœƒ
  • Bβˆ’1
  • Cβˆ’πœƒcos
  • D1

Q10:

Simplify sincossincosοŠͺοŠͺοŠ¨οŠ¨πœƒβˆ’πœƒπœƒβˆ’πœƒ.

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