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Hi can someone please illustrate to me how to dervive the half angle formulae from the compound angle formulae (or double angle formulae)? thanks

sin(a+b) = sin(a)cos(b) + cos(a)sin(b)

let b=a

sin(2a) = sin(a)cos(a) + cos(a)sin(a)

so

sin(2a) = 2sin(a)cos(a)

For the half angle formula. Let 2a = x

sin(x) = 2sin(0.5x)cos(0.5x)

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

let b=a

cos(2a) = cos²(a) - sin²(a)

= 2cos²(a) - 1

= 1 - 2sin²(a)

For the half angle formula. Let 2a = x

cos(x) = cos²(0.5x) - sin²(0.5x)

= 2cos²(0.5x) - 1

= 1 - 2sin²(0.5x)

let b=a

sin(2a) = sin(a)cos(a) + cos(a)sin(a)

so

sin(2a) = 2sin(a)cos(a)

For the half angle formula. Let 2a = x

sin(x) = 2sin(0.5x)cos(0.5x)

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

let b=a

cos(2a) = cos²(a) - sin²(a)

= 2cos²(a) - 1

= 1 - 2sin²(a)

For the half angle formula. Let 2a = x

cos(x) = cos²(0.5x) - sin²(0.5x)

= 2cos²(0.5x) - 1

= 1 - 2sin²(0.5x)

SsEe

sin(a+b) = sin(a)cos(b) + cos(a)sin(b)

let b=a

sin(2a) = sin(a)cos(a) + cos(a)sin(a)

so

sin(2a) = 2sin(a)cos(a)

For the half angle formula. Let 2a = x

sin(x) = 2sin(0.5x)cos(0.5x)

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

let b=a

cos(2a) = cos²(a) - sin²(a)

= 2cos²(a) - 1

= 1 - 2sin²(a)

For the half angle formula. Let 2a = x

cos(x) = cos²(0.5x) - sin²(0.5x)

= 2cos²(0.5x) - 1

= 1 - 2sin²(0.5x)

let b=a

sin(2a) = sin(a)cos(a) + cos(a)sin(a)

so

sin(2a) = 2sin(a)cos(a)

For the half angle formula. Let 2a = x

sin(x) = 2sin(0.5x)cos(0.5x)

cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

let b=a

cos(2a) = cos²(a) - sin²(a)

= 2cos²(a) - 1

= 1 - 2sin²(a)

For the half angle formula. Let 2a = x

cos(x) = cos²(0.5x) - sin²(0.5x)

= 2cos²(0.5x) - 1

= 1 - 2sin²(0.5x)

so which bit do you actually use?

sin(x) = 2sin(0.5x)cos(0.5x)

1 - 2sin²(0.5x)

i understand how you got these, but how do you then use them?

What unit is this?

melbourne

so which bit do you actually use?

sin(x) = 2sin(0.5x)cos(0.5x)

1 - 2sin²(0.5x)

i understand how you got these, but how do you then use them?

sin(x) = 2sin(0.5x)cos(0.5x)

1 - 2sin²(0.5x)

i understand how you got these, but how do you then use them?

We had a thread about the half-angle formulae a while ago, and decided, I think, by some kind of majority, that you don't really need them.

I can't remember having to use them.

Aitch

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- Trigonometry and identities
- TMUA
- physics Isaac physics question
- Trigonometry
- mirror equation
- Vectors help!
- gcse maths higher
- Physics
- math help alevel trigonometry
- Dee’s A*AA Journey
- How hard was A Level Mathematics?
- Addition Formulae Question
- Does anyone have a gcse maths topic list per paper?

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