Lesson Worksheet: Double- and Half-Angle Trigonometric Identities Mathematics

In this worksheet, we will practice evaluating trigonometric expressions using the double-angle and half-angle identities.

Q1:

Which of the following is equal to 12𝑥cos?

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

Q2:

Find the value of 27575sincos without using a calculator.

  • A12
  • B22
  • C12
  • D22

Q3:

Find, without using a calculator, the value of tan2𝐴 given sin𝐴=2425, where 0<𝐴<90.

  • A168527
  • B2352527
  • C48527
  • D336527

Q4:

Find, without using a calculator, the value of cos2𝐴 given csc𝐴=53 where 0<𝐴<90.

  • A725
  • B1625
  • C2425
  • D4325

Q5:

Simplify sinsin𝑥𝑥.

  • Asin2𝑥
  • Bcos2𝑥
  • C122𝑥cos
  • D142𝑥sin

Q6:

Find, without using a calculator, the value of tan𝐴 given tan2𝐴=34.

  • A3, 13
  • B3, 13
  • C3, 13
  • D3, 13

Q7:

Simplify 12𝑥1+2𝑥coscos.

  • Atan𝑥
  • Bcot2𝑥
  • Ctan2𝑥
  • Dcot𝑥

Q8:

Find, without using a calculator, the value of sin2𝐴 given cot𝐴=34 where 3𝜋2<𝐴<2𝜋.

  • A725
  • B925
  • C2425
  • D1225

Q9:

Evaluate cossin165165 without using a calculator.

  • A32
  • B14
  • C32
  • D34

Q10:

Find the value of cossin𝐴+2𝐵 given tan𝐴2=3 where 𝐴𝜋2,𝜋 and tan𝐵=15 where 𝐵0,𝜋2.

  • A2165
  • B813
  • C813
  • D2765
  • E2765

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