Prove Trigonometric Statement: Ideas & Solutions

[likearollings]

Homework Statement

Prove

http://img847.imageshack.us/img847/9428/trig.png

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Homework Equations

I am not quite sure how to prove this,

I can see it involves using a double angle formula (see http://mathworld.wolfram.com/Double-AngleFormulas.html).

The Attempt at a Solution

I have tried working backwards using a double angle formula but to no avail.

Any Ideas?

 

[Metaleer]

Have you tried mathematical induction?

 

[likearollings]

Have you tried mathematical induction?

Hi thanks for the reply,

No, don't know why I didn't think of that,

Will give it a go now.

 

[likearollings]

I don't think this is to be done with mathematical induction. I ended up with these massive identities and really long formulas,

Is there another way?

 

[likearollings]

I managed to do it using

$$\cos a \sin b = (\sin (a+b) - \sin(a-b))/2$$

PROBLEM SOLVED!

 

[icystrike]

Have u proven the P1 case and related Pk with Pk+1?

Do u think the identity below will help ?

$$sin(x)cos[(2k+1)x]$$
$$=\frac{sin[((2k+2)x)-((2k)x)]}{2} + \frac{cos[((2k+2)x)+((2k)x)]}{2}$$
$$=\frac{1}{2}[sin((2k+2)x)-sin((2k)x))]$$