# Trig identities

Gold Member

## Homework Statement

prove that, (cos(3x) - cos (7x)) / (sin(7x) + sin(3x)) = tan(2x)

prove that, cos(3x) = 4cos^3(x) - 3cos(x)

## Homework Equations

tan(x) = sin(x)/cos(x) must come into the first one

## The Attempt at a Solution

tried seperating the fraction so there is only one cos term on top, but I don't know how to deal with the sin terms on the bottom.

I haven't got a clue for the second one

Have you tried the sum-to product formula's?? (aka the Simpson formula's)

Gold Member
No I'm looking for them now, do you know that they work for these questions?

Gold Member
I still can't seem to get them right. My problem is not so much doing it, just working out which formular to use.

Gold Member
I'm still stuck on these. Can anyone point me in the right direction?

dextercioby
Homework Helper
Use the wiki page linked to above, especially this section

http://en.wikipedia.org/wiki/List_o...#Product-to-sum_and_sum-to-product_identities

$\cos 3x - \cos 7x$ can be reduced to a product of sines. Likewise the sum of sines in the denominator.

As for the other identity

$$\cos 3x = \cos (2x +x) = \left(\substack{\underbrace{\cos^2 x -\sin^2 x}\\ \cos 2x}\right) \cos x - \left(\substack{\underbrace{2\sin x \cos x}\\ \sin 2x}\right) \sin x = ...$$

The final result follows easily.

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Gold Member
I did the first one, but I'm still suck on the second one.

I ended up with cos(3x) = cos^3(x) - 3sin^2(x)cos(x), which is getting there, but I'm not sure what to do next

Try to change the sine into a cosine somehow... There's a really important formula which allow you to do that...