Cos (x-y)

------------ =

Cos (x+y)

1 + tanx tany

--------------

1 - tanx tany

and

Sin 3x=3sinx-4sin^3x

Any help would be greatly appreciated (Nod)

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- May 27th 2011, 08:14 PMmortifiedpenguinproofs - help
Cos (x-y)

------------ =

Cos (x+y)

1 + tanx tany

--------------

1 - tanx tany

and

Sin 3x=3sinx-4sin^3x

Any help would be greatly appreciated (Nod) - May 27th 2011, 08:50 PMChris L T521
- May 27th 2011, 08:56 PMJoanna
I would start with

and transform them into something to which you can apply the angle sum identities for cosine. (i.e. cos(x+y) = cos(x)cos(y)-sin(x)sin(y) and

cos(x-y)=cos(x)cos(y)+sin(x)sin(y) ) - May 28th 2011, 04:33 AMSoroban
Hello, mortifiedpenguin!

Quote:

We have: .

Divide numerator and denominator by

. .

- May 28th 2011, 05:16 PMipower94sin 3x=3sinx - 4sin^3x
sin 3x = sin( 2x +x )

= sin2xcosx + sinxcos2x

= (2sinxcosx)cosx + (cos^2x - sin^2x)sinx

= 2sinxcosx^2 + cos^2xsinx - sin^3x

= ...