Maths Extension 1 Year 11 - Module 3 - Lesson 6
Double Angle Formulas
Name
Date
Class
1. Lesson focus
Double-angle formulae. sin2x=2sinxcosx, cos2x=cos²x−sin²x=2cos²x−1=1−2sin²x, and tan2x=2tanx/(1−tan²x).
Success criteria
- Apply the lesson method accurately in a routine example.
- Show each algebraic or domain step and check the result.
- Explain why the method and restrictions fit the question.
2. Worked practice
2. If tan x=1/2, find tan2x.
3. Solve cos2x=0 for 0≤x<2π.
3. Challenge
Use a double-angle identity to simplify 2sin²(π/8).
4. Multiple choice
Which is a correct double-angle identity?
A. cos2x=2sinxcosx
B. sin2x=2sinxcosx
C. tan2x=tan²x−1
D. sin2x=sin²x−cos²x
Worked answer key
Compare each step with your working. Keep stated intervals, domains and restrictions in your final answer.
1. If cos x=3/5 and x is acute, find sin2x and cos2x.
sinx=4/5; sin2x=2(3/5)(4/5)=24/25 and cos2x=9/25−16/25=−7/25.
2. If tan x=1/2, find tan2x.
tan2x=2(1/2)/(1−1/4)=1/(3/4)=4/3.
3. Solve cos2x=0 for 0≤x<2π.
2x=π/2+kπ; within the interval x=π/4,3π/4,5π/4,7π/4.
Challenge. Use a double-angle identity to simplify 2sin²(π/8).
2sin²u=1−cos2u; result=1−cos(π/4)=1−√2/2.
Multiple choice. Which is a correct double-angle identity?
Correct answer: B. The sine double-angle formula is obtained from sin(x+x)=sinxcosx+cosxsinx.
Want help with Worksheet - Double Angle Formulas?
Tell us what you would like help with. Register interest; support details will be confirmed before enrolment.
Register interest →