Lesson Worksheet: Double-Angle and Half-Angle Identities Mathematics • 10th Grade

In this worksheet, we will practice using the double-angle and half-angle identities to evaluate trigonometric values.

Q1:

Use the addition formula to find an expression for sin2𝛼.

  • Asincossin2𝛼=𝛼+𝛼
  • Bsincossin2𝛼=2𝛼𝛼
  • Csincossin2𝛼=𝛼+𝛼
  • Dsincossin2𝛼=𝛼𝛼
  • Esincossin2𝛼=𝛼𝛼

Q2:

Find the value of 11+tantan without using a calculator.

  • A12
  • B12
  • C12
  • D12

Q3:

Find the value of 27575sincos without using a calculator.

  • A12
  • B22
  • C12
  • D22

Q4:

Which of the following is equal to 12𝑥cos?

  • A2|𝑥|sin
  • B|𝑥|sin
  • C2|𝑥|sin
  • D2|𝑥|cos
  • E2|𝑥|cos

Q5:

Simplify 12𝑥1+2𝑥coscos.

  • Atan𝑥
  • Bcot2𝑥
  • Ctan2𝑥
  • Dcot𝑥

Q6:

Find, without using a calculator, the value of sin2𝐴 given cos𝐴=1213 where 180𝐴<270.

  • A60169
  • B60169
  • C1013
  • D120169
  • E120169

Q7:

Simplify sinsin𝑥𝑥.

  • Asin2𝑥
  • Bcos2𝑥
  • C122𝑥cos
  • D142𝑥sin

Q8:

Find the value of cos𝜃2 given cos𝜃=1517 where 0<𝜃<90 without using a calculator.

  • A355
  • B41717
  • C31010
  • D1717

Q9:

Using the half angle formulas, or otherwise, find the exact value of tan𝜋8.

  • A1+2
  • B1+2
  • C12
  • D2
  • E12

Q10:

Find, without using a calculator, the value of sincos2𝐵22𝐵 given cos𝐵=45 where 3𝜋2<𝐵<2𝜋.

  • A67
  • B625
  • C127
  • D1225

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