1. ## Proving Identies

How do I prove this identity. The only thing I know is that I have to use a product to sum formula, but which one?

$\frac{cos 66 * cos 6 + cos 84 * cos 24}{cos 65 * cos 5 + cos 85 * cos 25}=1$

2. Originally Posted by HSS8
How do I prove this identity. The only thing I know is that I have to use a product to sum formula, but which one?

$\frac{cos 66 * cos 6 + cos 84 * cos 24}{cos 65 * cos 5 + cos 85 * cos 25}=1$
HI

$\frac{\frac{1}{2}[\cos 72+\cos 60]+\frac{1}{2}[\cos 108+\cos 60]}{\frac{1}{2}[\cos 70+\cos 60]+\frac{1}{2}[\cos 110+\cos 60]}$

$=\frac{\frac{1}{2}[\cos 72+\cos 108+2\cos 60]}{\frac{1}{2}[\cos 70+\cos 110+2\cos 60]}$

$=\frac{\frac{1}{2}[\cos 72+(-\cos 72)+2\cos 60]}{\frac{1}{2}[\cos 70+(-\cos 70)+2\cos 60]}$

so all these would cancel off to give you 1.

3. i thought only clues or a little help (not complete solution) will be given on the first day?

,

we will use this: , yes cos(A - B), you will see the pattern once you apply it.

Numerator = N = cos 66 cos 6 + cos 84 cos 24 = cos 66 cos 6 + sin 6 sin 66

Denominator = D = cos 65 cos 5 + sin 5 sin 65

N/D = ?